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Eurasian Math. J., 2013, Volume 4, Number 1, Pages 82–124 (Mi emj117)  

This article is cited in 32 scientific papers (total in 32 papers)

Smoothness spaces related to Morrey spaces — a survey. II

W. Sickel

Mathematishes Institut, Friedrich-Schiller-University, Jena, Germany

Abstract: We continue the discussion of different strategies of introducing smoothness spaces related to Morrey spaces.

Keywords and phrases: Morrey spaces, Nikol'skii–Besov spaces, Lizorkin–Triebel spaces, Nikol'skii–Besov type spaces, Lizorkin–Triebel type spaces, differences, wavelets, atoms, approximation spaces, Gagliardo–Nirenberg type inequalities, embeddings, real interpolation.

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MSC: 46E35
Received: 25.04.2012
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Citation: W. Sickel, “Smoothness spaces related to Morrey spaces — a survey. II”, Eurasian Math. J., 4:1 (2013), 82–124

Citation in format AMSBIB
\Bibitem{Sic13}
\by W.~Sickel
\paper Smoothness spaces related to Morrey spaces~--- a survey.~II
\jour Eurasian Math. J.
\yr 2013
\vol 4
\issue 1
\pages 82--124
\mathnet{http://mi.mathnet.ru/emj117}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3118894}
\zmath{https://zbmath.org/?q=an:1290.46028}


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    This publication is cited in the following articles:
    1. V. I. Burenkov, “Recent progress in studying the boundedness of classical operators of real analysis in general Morrey-type spaces. II”, Eurasian Math. J., 4:1 (2013), 21–45  mathnet  mathscinet  zmath
    2. V. I. Burenkov, D. K. Darbayeva, E. D. Nursultanov, “Description of interpolation spaces for general local Morrey-type spaces”, Eurasian Math. J., 4:1 (2013), 46–53  mathnet  mathscinet  zmath
    3. T. V. Tararykova, “Comments on definitions of general local and global Morrey-type spaces”, Eurasian Math. J., 4:1 (2013), 125–134  mathnet  mathscinet  zmath
    4. Haroske D.D., Skrzypczak L., “Embeddings of Besov-Morrey Spaces on Bounded Domains”, Studia Math., 218:2 (2013), 119–144  crossref  mathscinet  zmath  isi  scopus
    5. Yang D., Yuan W., Zhuo C., “Complex Interpolation on Besov-Type and Triebel-Lizorkin-Type Spaces”, Anal. Appl., 11:5 (2013), 1350021  crossref  mathscinet  zmath  isi  scopus
    6. V. I. Burenkov, E. D. Nursultanov, D. K. Chigambayeva, “Description of the interpolation spaces for a pair of local Morrey-type spaces and their generalizations”, Proc. Steklov Inst. Math., 284 (2014), 97–128  mathnet  crossref  crossref  isi  elib  elib
    7. Haroske D.D., Skrzypczak L., “On Sobolev and Franke-Jawerth Embeddings of Smoothness Morrey Spaces”, Rev. Mat. Complut., 27:2 (2014), 541–573  crossref  mathscinet  zmath  isi  scopus
    8. Sautbekova M., Sickel W., “Strong Summability of Fourier Series and Morrey Spaces”, Anal. Math., 40:1 (2014), 31–62  crossref  mathscinet  zmath  isi  elib  scopus
    9. Sickel W., Yang D., Yuan W., “The Radial Lemma of Strauss in the Context of Morrey Spaces”, Ann. Acad. Sci. Fenn. Ser. A1-Math., 39:1 (2014), 417–442  crossref  mathscinet  zmath  isi  scopus
    10. Yuan W., “Complex Interpolation For Predual Spaces of Morrey-Type Spaces”, Taiwan. J. Math., 18:5 (2014), 1527–1548  crossref  mathscinet  isi  scopus
    11. Triebel H., “Hybrid Function Spaces, Heat and Navier-Stokes Equations”, Hybrid Function Spaces, Heat and Navier-Stokes Equations, Ems Tracts in Mathematics, 24, Eur. Math. Soc., 2014, 1–185  mathscinet  isi
    12. de Almeida M.F., Precioso J.C.P., “Existence and Symmetries of Solutions in Besov-Morrey Spaces For a Semilinear Heat-Wave Type Equation”, J. Math. Anal. Appl., 432:1 (2015), 338–355  crossref  mathscinet  zmath  isi  scopus
    13. Yuan Wen Winfried S. Yang DaChun, “Interpolation of Morrey-Campanato and Related Smoothness Spaces”, Sci. China-Math., 58:9 (2015), 1835–1908  crossref  mathscinet  zmath  isi  scopus
    14. Yuan W., Haroske D.D., Skrzypczak L., Yang D., “Embedding Properties of Weighted Besov-Type Spaces”, Anal. Appl., 13:5 (2015), 507–553  crossref  mathscinet  zmath  isi  scopus
    15. Yuan W., Haroske D.D., Moura S.D., Skrzypczak L., Yang D., “Limiting Embeddings in Smoothness Money Spaces, Continuity Envelopes and Applications”, J. Approx. Theory, 192 (2015), 306–335  crossref  mathscinet  zmath  isi  elib  scopus
    16. Yuan W., Haroske D.D., Skrzypczak L., Yang D., “Embedding Properties of Besov-Type Spaces”, Appl. Anal., 94:2 (2015), 318–340  crossref  mathscinet  zmath  isi  scopus
    17. Yuan W., Lu Yu., Yang D., “Fractional Hajlasz-Morrey-Sobolev Spaces on Quasi-Metric Measure Spaces”, Studia Math., 226:2 (2015), 95–122  crossref  mathscinet  zmath  isi  scopus
    18. Yang D., Zhuo C., Yuan W., “Triebel-Lizorkin Type Spaces With Variable Exponents”, Banach J. Math. Anal., 9:4 (2015), 146–202  crossref  mathscinet  zmath  isi  scopus
    19. Triebel H., “Tempered Homogeneous Function Spaces”: Triebel, H, Tempered Homogeneous Function Spaces, Ems Series of Lectures in Mathematics, Eur. Math. Soc., 2015, COVER1–U6  mathscinet  isi
    20. L. Liu, D. Yang, W. Yuan, “Besov-type and Triebel-Lizorkin-type spaces associated with heat kernels”, Collect. Math., 67:2 (2016), 247–310  crossref  mathscinet  zmath  isi  scopus
    21. Sh. Nakamura, T. Noi, Y. Sawano, “Generalized Morrey spaces and trace operator”, Sci. China-Math., 59:2 (2016), 281–336  crossref  mathscinet  isi  elib  scopus
    22. D. D. Haroske, S. D. Moura, “Some specific unboundedness property in smoothness Morrey spaces. The non-existence of growth envelopes in the subcritical case”, Acta. Math. Sin.-English Ser., 32:2 (2016), 137–152  crossref  mathscinet  zmath  isi  scopus
    23. V. I. Burenkov, T. V. Tararykova, “An analog of Young's inequality for convolutions of functions for general Morrey-type spaces”, Proc. Steklov Inst. Math., 293 (2016), 107–126  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    24. W. Yuan, Yu.-f. Lu, D.-Yang, “Several equivalent characterizations of fractional Hajasz-Morrey-Sobolev spaces”, Appl. Math.-J. Chin. Univ. Ser. B, 31:3 (2016), 343–354  crossref  mathscinet  zmath  isi  scopus
    25. D. D. Haroske, S. D. Moura, L. Skrzypczak, “Smoothness Morrey spaces of regular distributions, and some unboundedness property”, Nonlinear Anal.-Theory Methods Appl., 139 (2016), 218–244  crossref  mathscinet  zmath  isi  scopus
    26. V. I. Burenkov, T. V. Tararykova, “Young’s inequality for convolutions in Morrey-type spaces”, Eurasian Math. J., 7:2 (2016), 92–99  mathnet
    27. D. D. Haroske, S. D. Moura, C. Schneider, L. Skrzypczak, “Unboundedness properties of smoothness Morrey spaces of regular distributions on domains”, Sci. China-Math., 60:12 (2017), 2349–2376  crossref  isi
    28. Z. Baituyakova, W. Sickel, “Strong summability of Fourier series and generalized Morrey spaces”, Anal. Math., 43:3 (2017), 371–414  crossref  isi
    29. D. D. Haroske, L. Skrzypczak, “Embeddings of weighted Morrey spaces”, Math. Nachr., 290:7 (2017), 1066–1086  crossref  isi
    30. D. D. Haroske, L. Skrzypczak, “Compact embeddings of weighted smoothness spaces of Morrey type: an example”, Functional Analysis, Harmonic Analysis, and Image Processing: a Collection of Papers in Honor of Bjorn Jawerth, Contemporary Mathematics, 693, eds. M. Cwikel, M. Milman, Amer. Math. Soc., 2017, 235–253  crossref  isi
    31. Z. A. Kasumov, N. R. Ahmedzade, “On the Dirichlet problem for the Laplace equation with the boundary value in Morrey space”, Eurasian Math. J., 9:4 (2018), 9–21  mathnet  crossref
    32. D. I. Hakim, “Complex interpolation of certain closed subspaces of generalized Morrey spaces”, Tokyo J. Math., 41:2 (2018), 487–514  crossref  mathscinet  zmath  isi  scopus
  • Eurasian Mathematical Journal
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