Universität Jena, Fakultät für Mathematik & Informatik [
Math-Net
] , Mathematisches
Institut
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 (to appear).
- 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 (1923 -)
https://doi.org/10.1007/s10231-023-01379-y.
-
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.