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...
Saved in:
| Published in: | Nagoya mathematical journal Vol. 242; pp. 1 - 34 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Nagoya
Cambridge University Press
01.06.2021
|
| Subjects: | |
| ISSN: | 0027-7630, 2152-6842 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0027-7630 2152-6842 |
| DOI: | 10.1017/nmj.2019.18 |