Winfried Sickel

List of Publications

(later than 1996)

• T. Runst and W. Sickel:   Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations. de Gruyter Series in Nonlinear Analysis and Applications 3, Berlin 1996, 547 p. .
• W. Sickel:   Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case $1\le s \le n/p$. Forum Math. 9 (1997), 267-302.
• K.V. Runovskii and W. Sickel:   Marcinkiewicz-Zygmund-type inequalities, trigonometric interpolation on non-uniform grids and unconditional Schauder bases in Besov spaces on the torus. Z. Anal. Anwendungen 16 (1997), 669-687.
• W. Sickel:   Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case $1\le s \le n/p$. II. Forum Math. 10 (1998), 199-231.
• W. Sickel:   Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case $1 \le s \le n/p$. III. Forum Math 10 (1998), 303-327.
• G. Bourdaud and W. Sickel:   Homeomorphisms which preserve Besov spaces. Math. Nachr. 198 (1999), 19-39.
• W. Sickel and A. Youssfi:   The characterization of the regularity of the Jacobian determinant in the framework of potential spaces. J. London Math. Soc. 59 (1999), 287- 310.
• W. Sickel:   On pointwise multipliers for $F^s_{p,q}({\bf R}^n)$ in case $\sigma_{p,q} < s < n/p$. Annali di Matematica Pura ed Applicata 174 (1999), 209-250.
• W. Sickel and A. Youssfi:   The characterization of the regularity of the Jacobian determinant in the framework of Bessel potential spaces on domains. J. London Math. Soc. 60 (1999), 561-580.
• W. Sickel and F. Sprengel:   Interpolation on sparse grids and Nikol´skij-Besov spaces of dominating mixed smoothness. J. of Computational Analysis and Applications 1 (1999), 263-288.
• W. Sickel:   Pointwise multipliers of Lizorkin-Triebel spaces. In: Operator Theory: Advances and Applications 110, pp. 295-321, Birkhäuser, Basel 1999.
• W. Sickel and F. Sprengel:   Some error estimates for periodic interpolation of functions from Besov spaces. Proc. Conf. Multivariate Approx. Theory, Witten-Bommerholz, 1998, Birkhäuser, Oper. Theory, Adv. Appl. 110 (1999), 295-321.
• W. Sickel:   Tensorproducts of periodic Besov spaces. Jenaer Schriften zur Mathematik und Informatik, Math/Inf/99/04.
• W. Sickel and Igor Smirnov:   Localization properties of Besov spaces and of its associated multiplier spaces. Jenaer Schriften zur Mathematik und Informatik, Math/Inf/99/21.
• W. Sickel:   Boundedness properties of the mapping $f \mapsto |f|^\mu, \, 0 < \mu < 1$, in the framework of Besov spaces. Preprint, Jena, 1999, 19 pages.
• J. Johnsen, W. Farkas and W. Sickel:   Traces of Besov-Lizorkin-Triebel spaces - a complete collection of all limiting cases. Math. Bohemica 125 (2000), 1-37.
• W. Sickel and L. Skrzypczak:   Radial subspaces of Besov and Lizorkin-Triebel classes: extended Strauss lemma and compactness of embeddings. J. Fourier Anal. Appl. 6 (2000), 639-662.
• H.-J. Schmeißer and W. Sickel:   Sampling theory and function spaces. In: Applied Mathematics Reviews (ed. G.A.Anastassiou) Vol. 1, 205-284, World Scientific, Singapore, 2000.
• W. Sickel:   Sampling on sparse grids and approximation spaces with respect to the hyperbolic cross. Proc. SampTA 2001, Univ. of Florida and IEEE (ed. A.I. Zayed), 275-279.
• H.-J. Schmeißer and W. Sickel:   Traces, Gagliardo-Nirenberg inequalities and Sobolev type embeddings for vector-valued function spaces. Jenaer Schriften zur Math. und Inf. Math/Inf/24/01, 58 pages.
• H. Koch and W. Sickel:   Pointwise multipliers of Besov spaces of smoothness zero and spaces of continuous functions. Rev. Mat. Iberoamericana 18 (2002), 587-626.
• G. Bourdaud, M. Lanza de Cristoforis and W. Sickel:   Functional calculus on BMO and related spaces. J. Functional Anal. 189 (2002), 515-538.
• W. Sickel:   Approximate recovery of functions and Besov spaces of dominating mixed smoothness. In: Constructive theory of functions, Varna 2002, DARBA, Sofia, 2003, 404-411.
• G. Bourdaud, M. Reissig and W. Sickel:   Hyperbolic equations, function spaces with exponential weights and Nemytskij operators. Annali di Matematica Pura ed Applicata 182 (2003), 409-455.
• T. Kühn, H.-G. Leopold, W. Sickel and L. Skrzypczak:   Entropy numbers of Sobolev embeddings of radial Besov spaces. J. Approx. Theory 121 (2003), 244-268.
• H.-J.Schmeißer and W. Sickel:   Spaces of functions of mixed smoothness and approximation from hyperbolic crosses. J. Appprox. Theory 128 (2004), 115-150.
• T. Kühn, H.-G. Leopold, W. Sickel and L. Skrzypczak:   Entropy numbers of embeddings of weighted Besov spaces. Math/Inf/13/03 (2003), 57 pp.
• H.-J.Schmeißer and W. Sickel: Vector-valued Sobolev spaces and Gagliardo-Nirenberg inequalities. In: Progress in nonlinear differential equations and their applications, 64, 463-472, Birkh\"auser, Basel, 2005.
• G. Bourdaud, M. Lanza de Cristoforis and W. Sickel:   Superposition operators and functions of bounded p-variation. Revista Mat. Iberoamericana 22 (2006), 455-487.
• G. Bourdaud, M. Lanza de Cristoforis and W. Sickel:   Superposition operators and functions of bounded p-variation II. J. Nonlinear Analysis 62 (2005), 483-517.
• S. Dahlke, E. Novak and W. Sickel:   Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings. J. of Complexity 22 (2006), 29-49.
• S. Dahlke, E. Novak and W. Sickel:   Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings. II J. of Complexity 22 (2006), 549-603.
• T. Kühn, H.-G. Leopold, W. Sickel and L. Skrzypczak:   Entropy numbers of embeddings of weighted Besov spaces. Constr. Approx. 23 (2006), 61-77.
• T. Kühn, H.-G. Leopold, W. Sickel and L. Skrzypczak:   Entropy numbers of embeddings of weighted Besov spaces. II. Proc. Edinburgh Math. Soc. 49 (2006), 331-359.
• T. Kühn, H.-G. Leopold, W. Sickel and L. Skrzypczak:   Entropy numbers of embeddings of weighted Besov spaces. III. Math. Zeitschrift 255 (2007), 1-15.
• W. Sickel:   Approximation from sparse grids and function spaces of dominating mixed smoothness. Banach Center Publ. 72 (2006), 271-283.
• J. Johnsen and W. Sickel:   A direct proof of Sobolev embeddings for quasi-homogeneous Lizorkin-Triebel spaces with mixed norms. JFSA 5 (2007), 183-198.
• J. Vybiral and W. Sickel:   Traces of functions with a dominating mixed derivative in R^3. Czechoslovak Math. J. 57 (132) (2007), 1239-1273.
• G. Bourdaud, M. Moussai and W. Sickel:   Towards sharp superposition theorems in Besov and Lizorkin-Triebel spaces. J. Nonlinear Analysis 68 (2008), 2889-2912.
• G. Bourdaud, M. Moussai and W. Sickel:   On optimal symbolic calculus on Besov Algebras. Annales de l'I.H.P. - AN 23 (2006), 949-956.
• S. Dahlke, E. Novak and W. Sickel:   Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings III: Frames. Journal of Complexity 23 (2007), 614-648.
• J. Johnsen and W. Sickel:   On the trace problem for Lizorkin-Triebel spaces with mixed norms. Math. Nachr. 281 (2008), 669-696.
• W. Sickel and T. Ullrich:   Smolyak's Algorithm, Sampling on Sparse Grids and Function Spaces of Dominating Mixed Smoothness. Jenaer Schriften zur Math. und Inf. Math/Inf/14/06, 57 pages.
• W. Sickel and T. Ullrich:   Smolyak's Algorithm, Sampling on Sparse Grids and Function Spaces of Dominating Mixed Smoothness. East Journal on Approximation 13 (2007), 387-425.
• W. Sickel and T. Ullrich:   Tensor products of Sobolev-Besov spaces and applications to approximation from the hyperbolic cross. JAT 161 (2009), 748-786.
• S. Dahlke and W. Sickel:   Besov Regularity for the Poisson Equation in Smooth and Polyhedral Cones. In: Sobolev spaces in Mathematics II (ed. V.G.Maz'ya), Springer, 2009, pp. 123-145.
• S. Dahlke, E. Novak and W. Sickel:   Optimal Approximation of Elliptic Problems by Linear and Nonlinear Mappings IV: Errors in $L_2$ and other Norms. Journal of Complexity 26 (2010), 102-124.
• G. Bourdaud, M. Moussai and W. Sickel:   Composition operators on Lizorkin-Triebel spaces. Journal of Functional Anal. 259 (2010), 1098-1128.
• M. Hansen and W. Sickel:   Best m-term approximation and Lizorkin-Triebel spaces. JAT 163 (2011), 923-954.
• Preprint 22 (2009), 39 Seiten, DFG-Schwerpunktprogramm 1324.
• W. Sickel and T. Ullrich:   Spline interpolation on sparse grids. Applicable Analysis 90 (2011), 337-383.
• M. Hansen and W. Sickel,  Best $m$-term approximation and tensor products of Sobolev and Besov spaces -- the case of noncompact embeddings, East Journal on Approximations 16 (2010), 313-356.
• M. Hansen and W. Sickel,  Best $m$-term approximation and tensor products of Sobolev and Besov spaces -- the case of compact embeddings, Constructive Approximation 36 (2012), 1- 51.
• W. Yuan, W. Sickel and D. Yang:  Morrey and Campanato meet Besov, Lizorkin and Triebel, Lecture Notes in Math. 2005, Springer, Berlin, 2010.
• G.  Bourdaud and W. Sickel,   Composition operators on function spaces with fractional order of smoothness,   RIMS Kokyuroku Bessatsu B26 (2011), 93-132.
  
• Preprint of this paper: Paris/Jena 2010   pdf
• W. Sickel, L. Skrzypczak and J. Vybiral:   On the interplay of regularity and decay in case of radial functions I. Inhomogeneous spaces. Comm. in Contemp. Math. 14, No. 1 (2012), DOI: 10.1142/S0219199712500058.
• W. Sickel and L. Skrzypczak:   On the interplay of regularity and decay in case of radial functions II. Homogeneous spaces. JFAA  18 (2012), 548 - 582.
  
• S. Dahlke and W. Sickel:   On Besov Regularity of solutions to nonlinear elliptic partial differential equations. Revista Mat. Complutense 26 (2013), 115 - 145.
• W. Sickel:   Radial subspaces of Besov-Lizorkin-Triebel spaces. Proceedings Nonlinear Analysis, Function Spaces and Applications 9 (ed. by J.~Rakosnik), Inst. of Math. AS CR, 2011, 169-215.
• Preprint of this paper: Jena 2011   pdf
• B. Scharf, H.-J. Schmeißer and W. Sickel:   Traces of vector-valued Sobolev spaces. Math. Nachr. 285 (2012), 1082 - 1106.
• W. Sickel:   Smoothness spaces related to Morrey spaces.  Jena 2012, 71 pp.
• Preprint of this paper:    pdf
• J. Johnsen, S. Munch Hansen and W. Sickel: Characterization by local means of anisotropic Lizorkin-Triebel spaces with mixed norms, ZAA  32 (2013), 257 - 277.
• Preprint of this paper:    pdf
• G. Bourdaud, M. Moussai and W. Sickel:   Composition operators acting on Besov spaces on the real line.  Annali di Matematica Pura ed Applicata 193 (2014), 1519-1554.
  
• W. Sickel, L. Skrzypczak and J. Vybiral:   The Characterization of Radial Subspaces of Besov- and Lizorkin-Triebel Spaces by Differences, Proc. Conference Function spaces X, Poznan, 2012
• W. Sickel, L. Skrzypczak and J. Vybiral:   Complex Interpolation of weighted Besov- and Lizorkin-Triebel Spaces, (extended version) arxiv.org/abs/1212.1614
• W. Sickel, L. Skrzypczak and J. Vybiral:   Complex Interpolation of weighted Besov- and Lizorkin-Triebel Spaces, Math. Sinica 30 (2014), 1297-1323.
  
• W. Sickel and L. Skrzypczak:   Subradial Functions and Compact Embeddings, Proc. Steklov Institute of Math. Vol. 284  (2014), 216-234.
• W. Yuan, W. Sickel and D. Yang   The Radial Lemma of Strauss in the Context of Morrey Spaces, Annales Acad. Sci. Fennicae Math. 39 (2014), 1-26.
  
• W. Yuan, W. Sickel and D. Yang   Compact Embeddings for Radial and Subradial Subspaces of some Besov-type spaces related to Morrey spaces,  JAT  174 (2013), 121 - 139.
• W. Yuan, W. Sickel and D. Yang   On the coincidence of certain approaches to smoothness spaces related  Morrey spaces, Math. Nachr.  286 (2013), 1571 - 1584.
• W. Sickel:   Smoothness spaces related to Morrey spaces - a survey. I.  Eurasian Math. J. 3(3) (2012), 110-149.
• T. Kühn, W. Sickel and T. Ullrich:  Approximation numbers of Sobolev embeddings - sharp constants and tractability.  Journal of Complexity  30 (2014), 95-116.
• W. Sickel:   Smoothness spaces related to Morrey spaces - a survey. II.  Eurasian Math. J. 4(1) (2013), 82-124.
• Merey Sautbekova and W. Sickel :   Strong summability of Fourier series and Morrey spaces.  Analysis Mathematica 40 (2014), 31-62.
• J. Johnsen, S. Munch Hansen and W. Sickel: Anisotropic, mixed-norm Lizorkin-Triebel spaces and diffeomorphic maps, J. Function Spaces and Appl.  Vol. 2014, Article ID 964794, 
• http://dx.doi.org/10.1155/2014/964794.
  
• T. Kühn, W. Sickel and T. Ullrich:  Approximation of mixed order Sobolev functions on the $d$-torus -- asymptotics, preasymptotics and $d$-dependence. Constructive Approximation 42 (2015), 353 - 398.
  
• G. Byrenheid, Dinh D\~ung, W. Sickel and T. Ullrich:  Sampling on energy-norm based sparse grids for the optimal recovery of Sobolev type functions in $H^\gamma$. JAT 207 (2016), 207 - 231.
  
• W. Yuan, W. Sickel and D. Yang:   Interpolation of Morrey-Campanato and Related Smoothness Spaces. Science China Math. 59 (9)  (2015), 1835-1908.
• K. van Nguyen and W. Sickel:   Weyl numbers of embeddings of tensor product Besov spaces, JAT 200 (2015), 170 - 220.
• P. Mironescu and W. Sickel, A Sobolev non embedding, Rend. Lincei Mat. Appl. 26(3) (2015), 291–298.
• J. Johnsen, S. Munch Hansen and W. Sickel: Anisotropic Lizorkin-Triebel spaces with mixed norms - traces on smooth boundaries, Math. Nachr. 288 (11-12) (2015), 1327 -1359.
• M.Reich, M.Reissig and W.Sickel: Non-analytic Superposition Results on Modulation Spaces with Subexponential Weights, Journal of Pseudo-Differential Operators and Applications, 7 (2016), 365 - 402.  ArXiv 1510.07521.
  
• M.Reich and W. Sickel: Multiplication and Composition in  Weighted Modulation Spaces, In: Mathematical Analysis, Probability and Applications - Plenary Lectures, ISAAC 2015,
  
• Macau, Springer Proceedings in Mathematics and Statistics, Springer, 2016, 103 - 149,  ArXiv 1602.00280.
• K. van Nguyen and W. Sickel:   Isotropic and Dominating Mixed Besov Spaces -- a Comparison. Contemporary Mathematics 693 (2017), 363-389.  ArXiv 1601.04000v1.
• T. Kühn, F. Cobos and  W. Sickel:  Optimal approximation of multivariate periodic Sobolev functions in the sup-norm. J. Functional Anal. 270 (2016), 4196-4212.
• C. Zhuo,  W. Sickel, D. Yang and W. Yuan   Characterizations of Besov-Type and Triebel-Lizorkin-type spaces via averages on balls.  Canadian Math. Bull. 60 (3)(2017), 655-672.
• K. van Nguyen and W. Sickel:   Isotropic and dominating mixed Lizorkin-Triebel spaces -- a comparison. Analysis Mathematica  43 (2) (2017), 303-337.
• K. van Nguyen and W. Sickel:  Pointwise multipliers for Sobolev and Besov spaces of dominating mixed smoothness. JMAA 452 (2017), 62-90.
  
• K. van Nguyen and W. Sickel:  On a problem of Jaak Peetre concerning pointwise multipliers of Besov spaces. Studia Mathematica 243 (2018), 207-231. 
• Z. Baituyakova and W. Sickel :   Strong summability of Fourier series and Morrey spaces. II.   Analysis Mathematica 43 (3) (2017), 371-414.
• K. van Nguyen and W. Sickel:  Pointwise multipliers for Sobolev and Besov spaces of dominating mixed smoothness - II. Science China Math. 60 (2017), 2241-2262.
• T. Kühn, F. Cobos and  W. Sickel:  On optimal approximation in periodic Besov spaces. JMAA 474 (2019), 1441-1462.
• S. Dahlke, M. Hansen, C. Schneider and W. Sickel: On Besov regularity of solutions to  nonlinear elliptic partial differential equations. Nonlinear Analysis 192 (2020), 111682, 35 pp.
• W. Yuan, W. Sickel and D. Yang: Regularity Properties of the  Haar System with Respect to Besov-type Spaces,  Studia Math. 253 (2020) no. 2, 129-162.
• G. Bourdaud, M. Moussai and W. Sickel:  A necessary condition for composition in  Besov spaces.  Complex Variables and Elliptic Equations 65 65 (2020), no. 1, 22-39.
• T. Kühn, W. Sickel and T. Ullrich: How anisotropic mixed smoothness affects the decay of singular numbers of Sobolev embeddings. Journal of Complexity 63, no. 101523, 37 pp. .
• W. Sickel: On the regularity of characteristic functions. In:  Anomalies in Partial Differential Equations, Springer, Cham, INdAM Ser. 43 (2021), 395-441.
• Preprint of this paper:   pdf
• M. Hovemann  and W. Sickel: Besov-type spaces and differences. Eurasian Math J.  11 (1)(2020), 25-56.
• C. Zhuo, M. Hovemann  and W. Sickel: Complex Interpolation of Lizorkin-Triebel-Morrey Spaces on Domains. Anal. Geom. Metr. Spaces 8 (2020), no. 1, 268-304.
• W. Sickel: On a limiting case for pointwise multiplication in Nikol'skii-Besov spaces Tr. Mat. Inst. Steklova 312 (2021), 170-187.
• S. Yang, W. Sickel, D. Yang and W. Yuan: Regularity for Robin boundary problems of Laplace equations and Hardy spaces on C1 and (semi-)convex domains. J. Differential Equations 279 (2021), 198-244.
• Van Dung Nguyen, Van Kien Nguyen and W. Sickel: Widths of weighted Wiener classes. J. Approx. Theory 279 (2022), No. 105745, 26 pp.
• W. Sickel: On the regularity of characteristic functions of weakly exterior thick domains. Proc. Steklov Institute 323 (2023), 130-158.
• Z. Li, W. Sickel, D. Yang and W. Yuan: Pointwise multipliers for Besov spaces $B^{0,b}_{p,\infty} (R^n)$ with only logarithmic smoothness. Annali di Matematica Pura ed Applicata (4)203 (2024) no.2, 703-763.
• Y. Li, W. Sickel, D. Yang and W. Yuan: Characterizations of pointwise multipliers of Besov spaces in endpoint cases with an application to the duality principle J. Funct. Anal. 286 (2024), no. 1, No. 110198.
• Y. Li, W. Sickel, D. Yang and W. Yuan: Wavelet and Fourier analytic characterizations of pointwise multipliers of Besov spaces B^s_{p,p}(R^n) with 0287 (2024), no. 12, No. 110654.
• Yuan, Wen; Sickel, Winfried; Yang, Dachun: Regularity of Characteristic Functions in Besov-Type and Triebel?Lizorkin-Type Spaces. J. Fourier Anal. Appl. 31 (2025), no. 3, Paper No. 25.