Abstract:
We show that the calculation of the sum of local Morrey spaces can be reduced to the calculation of the sum of sequence spaces that appear as parameters in the definition of local Morrey spaces. The presence of such a reduction allows us to obtain new extrapolation theorems for local Morrey spaces with sharp constants.
Keywords:
Banach ideal space, local Morrey spaces, sum and intersection of spaces, extrapolation theorems.
Citation:
E. I. Berezhnoi, “Sharp Extrapolation Theorems for Local Morrey Spaces”, Function Spaces, Approximation Theory, and Related Problems of Analysis, Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii, Trudy Mat. Inst. Steklova, 312, Steklov Math. Inst., Moscow, 2021, 82–97; Proc. Steklov Inst. Math., 312 (2021), 76–90
\Bibitem{Ber21}
\by E.~I.~Berezhnoi
\paper Sharp Extrapolation Theorems for Local Morrey Spaces
\inbook Function Spaces, Approximation Theory, and Related Problems of Analysis
\bookinfo Collected papers. In commemoration of the 115th anniversary of Academician Sergei Mikhailovich Nikol'skii
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 312
\pages 82--97
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4126}
\crossref{https://doi.org/10.4213/tm4126}
\elib{https://elibrary.ru/item.asp?id=46015877}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 312
\pages 76--90
\crossref{https://doi.org/10.1134/S0081543821010041}
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Linking options:
https://www.mathnet.ru/eng/tm4126
https://doi.org/10.4213/tm4126
https://www.mathnet.ru/eng/tm/v312/p82
This publication is cited in the following 7 articles:
Evgenii I. Berezhnoi, “ABOUT THE RELATIONSHIP BETWEEN GRAND AND SMALL LEBESQUE SPACES WITH CLASSIC SYMMETRICAL SPACES”, J Math Sci, 2025
Evgenii I. Berezhnoi, “Multipliers for Pairs of Grand and Small Lebesgue Space for p∈(1,∞)”, Potential Anal, 2025
Evgenii I. Berezhnoi, “Multipliers for Pairs of Grand or Small Lebesque Spaces in Limiting Cases (p=1 or p=∞)”, Complex Anal. Oper. Theory, 19:3 (2025)
Evgeny Berezhnoi, Alexey Karapetyants, “Grand and small norms in Lebesgue spaces”, Math Methods in App Sciences, 47:2 (2024), 725
E. I. Berezhnoi, “The Calderón's Construction for Pairs of Grand and Small Lebesque Spaces”, Lobachevskii J Math, 45:12 (2024), 6060
E. I. Berezhnoi, V. V. Kocherova, “On extrapolation of compactness”, J. Math. Sci., 271:6 (2023), 786
E. I. Berezhnoi, A. N. Karapetyants, “A New Approach to Grand and Small Norms in Discrete Lebesgue Spaces”, Math. Notes, 114:6 (2023), 1118–1133
Citation in format AMSBIB
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