Maximal functions, Riesz potentials and Sobolev embeddings on Musielak-Orlicz-Morrey spaces of variable exponent in ${\bf R}^{n}$

2011 ◽  
Vol 25 (2) ◽  
pp. 413-434 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Eiichi Nakai ◽  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Variable Exponent ◽  
Morrey Spaces ◽  
Maximal Functions ◽  
Riesz Potentials ◽  
Sobolev Embeddings

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

2019 ◽  
pp. 1-34 ◽  
Author(s):  
YOSHIHIRO MIZUTA ◽  
TAKAO OHNO ◽  
TETSU SHIMOMURA
Keyword(s):  
Unit Ball ◽  
Variable Exponent ◽  
Type Inequality ◽  
Morrey Spaces ◽  
Maximal Functions ◽  
Sobolev Type ◽  
Riesz Potentials ◽  
Hölder Continuous ◽  
Double Phase ◽  
Sobolev Type Inequality

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.

Riesz potentials and Sobolev embeddings on Morrey spaces of variable exponents

2011 ◽  
Vol 56 (7-9) ◽  
pp. 671-695 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Eiichi Nakai ◽  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Variable Exponents ◽  
Riesz Potentials ◽  
Sobolev Embeddings

scholarly journals Sobolev Embeddings for Generalized Riesz Potentials of Functions in Morrey Spaces over Nondoubling Measure Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Yoshihiro Sawano ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Riesz Potentials ◽  
Sobolev Embeddings ◽  
Measure Spaces ◽  
Nondoubling Measure

Our aim in this paper is to deal with the Sobolev embeddings for generalized Riesz potentials of functions in Morrey spaces over nondoubling measure spaces.

Weighted Morrey spaces of variable exponent and Riesz potentials

2014 ◽  
Vol 288 (8-9) ◽  
pp. 984-1002 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Tetsu Shimomura
Keyword(s):  
Variable Exponent ◽  
Morrey Spaces ◽  
Riesz Potentials ◽  
Weighted Morrey Spaces
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