HERZ–MORREY SPACES ON THE UNIT BALL WITH VARIABLE EXPONENT APPROACHING AND DOUBLE PHASE FUNCTIONALS

Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent $p_{1}(\cdot )$ approaching $1$ and for double phase functionals $\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}$ , where $a(x)^{1/p_{2}}$ is nonnegativ...

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Published in:Nagoya mathematical journal Vol. 242; pp. 1 - 34
Main Authors: MIZUTA, YOSHIHIRO, OHNO, TAKAO, SHIMOMURA, TETSU
Format: Journal Article
Language:English
Published: Nagoya Cambridge University Press 01.06.2021
Subjects:
Euclidean space
Mathematical functions
ISSN:0027-7630, 2152-6842
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Abstract Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent $p_{1}(\cdot )$ approaching $1$ and for double phase functionals $\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}$ , where $a(x)^{1/p_{2}}$ is nonnegative, bounded and Hölder continuous of order $\unicode[STIX]{x1D703}\in (0,1]$ and $1/p_{2}=1-\unicode[STIX]{x1D703}/N>0$ . We also establish Sobolev type inequality for Riesz potentials on the unit ball.
AbstractList Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent \(p_{1}(\cdot )\) approaching \(1\) and for double phase functionals \(\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}\), where \(a(x)^{1/p_{2}}\) is nonnegative, bounded and Hölder continuous of order \(\unicode[STIX]{x1D703}\in (0,1]\) and \(1/p_{2}=1-\unicode[STIX]{x1D703}/N>0\). We also establish Sobolev type inequality for Riesz potentials on the unit ball.
Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent $p_{1}(\cdot )$ approaching $1$ and for double phase functionals $\unicode[STIX]{x1D6F7}_{d}(x,t)=t^{p_{1}(x)}+a(x)t^{p_{2}}$ , where $a(x)^{1/p_{2}}$ is nonnegative, bounded and Hölder continuous of order $\unicode[STIX]{x1D703}\in (0,1]$ and $1/p_{2}=1-\unicode[STIX]{x1D703}/N>0$ . We also establish Sobolev type inequality for Riesz potentials on the unit ball.
Author SHIMOMURA, TETSU
MIZUTA, YOSHIHIRO
OHNO, TAKAO
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Snippet Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent $p_{1}(\cdot )$...
Our aim in this paper is to deal with integrability of maximal functions for Herz–Morrey spaces on the unit ball with variable exponent \(p_{1}(\cdot )\)...
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SubjectTerms Euclidean space
Mathematical functions
Title HERZ–MORREY SPACES ON THE UNIT BALL WITH VARIABLE EXPONENT APPROACHING AND DOUBLE PHASE FUNCTIONALS
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