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Tr. Mat. Inst. Steklova, 2010, Volume 269, Pages 52–62 (Mi tm2891)  

This article is cited in 21 scientific papers (total in 21 papers)

Description of interpolation spaces for local Morrey-type spaces

V. I. Burenkov, E. D. Nursultanov

L. N. Gumilyov Eurasian National University, Astana, Kazakhstan

Abstract: We consider the real interpolation method and prove that for local Morrey spaces, in the case when they have the same integrability parameter, the interpolation spaces are again local Morrey-type spaces with appropriately chosen parameters. Thus, in contrast to the standard Morrey-type spaces, these local spaces form an interpolation scale. In particular, this is true in the so-called nondiagonal case.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2010, 269, 46–56

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UDC: 517.51+517.98
Received in December 2009

Citation: V. I. Burenkov, E. D. Nursultanov, “Description of interpolation spaces for local Morrey-type spaces”, Function theory and differential equations, Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday, Tr. Mat. Inst. Steklova, 269, MAIK Nauka/Interperiodica, Moscow, 2010, 52–62; Proc. Steklov Inst. Math., 269 (2010), 46–56

Citation in format AMSBIB
\by V.~I.~Burenkov, E.~D.~Nursultanov
\paper Description of interpolation spaces for local Morrey-type spaces
\inbook Function theory and differential equations
\bookinfo Collected papers. Dedicated to Academician Sergei Mikhailovich Nikol'skii on the occasion of his 105th birthday
\serial Tr. Mat. Inst. Steklova
\yr 2010
\vol 269
\pages 52--62
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\jour Proc. Steklov Inst. Math.
\yr 2010
\vol 269
\pages 46--56

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    This publication is cited in the following articles:
    1. M. I. Dyachenko, “Local smoothness of the conjugate functions”, Eurasian Math. J., 2:2 (2011), 31–59  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. Lemarie-Rieusset P.G., “Multipliers and Morrey Spaces”, Potential Anal., 38:3 (2013), 741–752  crossref  mathscinet  zmath  isi  elib  scopus
    7. 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
    8. 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
    9. Mustafayev R.Ch., Unver T., “Embeddings Between Weighted Local Morrey-Type Spaces and Weighted Lebesgue Spaces”, J. Math. Inequal., 9:1 (2015), 277–296  crossref  mathscinet  zmath  isi  elib  scopus
    10. Kussainova L. Ospanova A., “Interpolation Theorems For Weighted Sobolev Spaces”, World Congress on Engineering, Wce 2015, Vol i, Lecture Notes in Engineering and Computer Science, ed. Ao S. Gelman L. Hukins D. Hunter A. Korsunsky A., Int Assoc Engineers-Iaeng, 2015, 25–28  isi
    11. Hakim D.I., Sawano Y., “Interpolation of generalized Morrey spaces”, Rev. Mat. Complut., 29:2 (2016), 295–340  crossref  mathscinet  zmath  isi  scopus
    12. Nakai E., Sobukawa T., “$B_w^u$-function Spaces and Their Interpolation”, Tokyo J. Math., 39:2 (2016), 483–516  crossref  mathscinet  zmath  isi  scopus
    13. E. I. Berezhnoi, “A discrete version of local Morrey spaces”, Izv. Math., 81:1 (2017), 1–28  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    14. A. Gogatishvili, R. Mustafayev, T. Ünver, “Embedding relations between weighted complementary local Morrey-type spaces and weighted local Morrey-type spaces”, Eurasian Math. J., 8:1 (2017), 34–49  mathnet
    15. Hakim D.I., Sawano Y., “Caldern'S First and Second Complex Interpolations of Closed Subspaces of Morrey Spaces”, J. Fourier Anal. Appl., 23:5 (2017), 1195–1226  crossref  mathscinet  zmath  isi  scopus
    16. Hakim D.I., Nakamura Sh., Sawano Y., “Complex Interpolation of Smoothness Morrey Subspaces”, Constr. Approx., 46:3 (2017), 489–563  crossref  mathscinet  zmath  isi  scopus
    17. Guliyev V.S., Hasanov S.G., Sawano Y., “Decompositions of Local Morrey-Type Spaces”, Positivity, 21:3 (2017), 1223–1252  crossref  mathscinet  zmath  isi  scopus
    18. Hakim D.I., Nakamura Sh., Sawano Y., Sobukawa T., “Complex Interpolation of B-W(U)-Spaces”, Complex Var. Elliptic Equ., 63:4 (2018), 569–590  crossref  mathscinet  zmath  isi  scopus
    19. V. I. Burenkov, D. K. Chigambayeva, E. D. Nursultanov, “Marcinkiewicz-Type Interpolation Theorem and Estimates For Convolutions For Morrey-Type Spaces”, Eurasian Math. J., 9:2 (2018), 82–88  mathnet  isi
    20. Hakim D.I., “Complex Interpolation of Predual Spaces of General Local Morrey-Type Spaces”, Banach J. Math. Anal., 12:3 (2018), 541–571  crossref  mathscinet  isi
    21. Hakim D.I., “Complex Interpolation of Certain Closed Subspaces of Generalized Morrey Spaces”, Tokyo J. Math., 41:2 (2018), 487–514  crossref  mathscinet  isi
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