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Eurasian Math. J., 2012, Volume 3, Number 3, Pages 110–149 (Mi emj98)  

This article is cited in 44 scientific papers (total in 44 papers)

Smoothness spaces related to Morrey spaces – a survey. I

W. Sickel

Mathematishes Institut, Fridrich-Shiller University, Jena, Germany

Abstract: We discuss different strategies to introduce smoothness spaces related to Morrey spaces.

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

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Document Type: Article
MSC: 46E35
Received: 25.04.2012
Language: English

Citation: W. Sickel, “Smoothness spaces related to Morrey spaces – a survey. I”, Eurasian Math. J., 3:3 (2012), 110–149

Citation in format AMSBIB
\by W.~Sickel
\paper Smoothness spaces related to Morrey spaces~-- a~survey.~I
\jour Eurasian Math. J.
\yr 2012
\vol 3
\issue 3
\pages 110--149

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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. I”, Eurasian Math. J., 3:3 (2012), 11–32  mathnet  mathscinet  zmath
    2. 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
    3. 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
    4. W. Sickel, “Smoothness spaces related to Morrey spaces — a survey. II”, Eurasian Math. J., 4:1 (2013), 82–124  mathnet  mathscinet  zmath
    5. 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
    6. Yang Da-chun, Yuan Wen, “Function Spaces of Besov-Type and Triebel-Lizorkin-Type - a Survey”, Appl. Math.-J. Chin. Univ. Ser. B, 28:4 (2013), 405–426  crossref  mathscinet  zmath  isi  scopus
    7. 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
    8. Yuan W., Sickel W., Yang D., “On the Coincidence of Certain Approaches to Smoothness Spaces Related to Morrey Spaces”, Math. Nachr., 286:14-15 (2013), 1571–1584  crossref  mathscinet  zmath  isi  scopus
    9. Yuan W., Sickel W., Yang D., “Compact Embeddings of Radial and Subradial Subspaces of Some Besov-Type Spaces Related to Morrey Spaces”, J. Approx. Theory, 174 (2013), 121–139  crossref  mathscinet  zmath  isi  scopus
    10. 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
    11. Triebel H., “Local Function Spaces, Heat and Navier-Stokes Equations”, Local Function Spaces, Heat and Navier-Stokes Equations, Ems Tracts in Mathematics, 20, Eur. Math. Soc., 2013, 1–232  crossref  mathscinet  zmath  isi
    12. 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
    13. 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
    14. Zhuo C., Yang D., Yuan W., “Hausdorff Besov-Type and Triebel-Lizorkin-Type Spaces and their Applications”, J. Math. Anal. Appl., 412:2 (2014), 998–1018  crossref  mathscinet  zmath  isi  scopus
    15. 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
    16. 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
    17. Yuan W., “Complex Interpolation For Predual Spaces of Morrey-Type Spaces”, Taiwan. J. Math., 18:5 (2014), 1527–1548  crossref  mathscinet  isi  scopus
    18. 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
    19. 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
    20. 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
    21. 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
    22. 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
    23. 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
    24. 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
    25. 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
    26. Drihem D., “Some Properties of Variable Besov-Type Spaces”, Funct. Approx. Comment. Math., 52:2 (2015), 193–221  crossref  mathscinet  zmath  isi  scopus
    27. Triebel H., “Tempered Homogeneous Function Spaces”, Ems Series of Lectures in Mathematics, Eur. Math. Soc., 2015, COVER1–U6  mathscinet  isi
    28. 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
    29. 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
    30. 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
    31. 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
    32. 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
    33. 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
    34. V. I. Burenkov, T. V. Tararykova, “Young’s inequality for convolutions in Morrey-type spaces”, Eurasian Math. J., 7:2 (2016), 92–99  mathnet
    35. D.-Ch. Chang, D. Yang, W. Yuan, J. Zhang, “Some recent developments of high order Sobolev-type spaces”, J. Nonlinear Convex Anal., 17:9 (2016), 1831–1865  mathscinet  zmath  isi
    36. 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
    37. Z. Baituyakova, W. Sickel, “Strong summability of fourier series and generalized Morrey spaces”, Anal. Math., 43:3 (2017), 371–414  crossref  isi
    38. C. Zhuo, W. Sickel, D. Yang, W. Yuan, “Characterizations of Besov-type and Triebel-Lizorkin-type spaces via averages on balls”, Can. Math. Bul.-Bul. Can. Math., 60:3 (2017), 655–672  crossref  isi
    39. S. Wu, D. Yang, W. Yuan, “Equivalent quasi-norms of Besov-Triebel-Lizorkin-type spaces via derivatives”, Results Math., 72:1-2 (2017), 813–841  crossref  isi
    40. D. D. Haroske, L. Skrzypczak, “Embeddings of weighted Morrey spaces”, Math. Nachr., 290:7 (2017), 1066–1086  crossref  isi
    41. A. EL Baraka, M. Toumlilin, “Global well-posedness and decay results for 3D generalized magneto-hydrodynamic equations in critical Fourier-Besov-Morrey spaces”, Electron. J. Differ. Equ., 2017, 65  isi
    42. J. Zhang, C. Zhuo, D. Yang, Z. He, “Littlewood-Paley characterizations of Triebel-Lizorkin-Morrey spaces via ball averages”, Nonlinear Anal.-Theory Methods Appl., 150 (2017), 76–103  crossref  isi
    43. 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
    44. N. R. Ahmedzade, Z. A. Kasumov, “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
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