Sobolev's inequality for Riesz potentials of functions in grand Musielak-Orlicz-Morrey spaces over nondoubling metric measure spaces

2018 ◽  
Vol 291 (10) ◽  
pp. 1547-1562
Author(s):  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Metric Measure Spaces ◽  
Riesz Potentials ◽  
Sobolev’S Inequality ◽  
Measure Spaces

Sobolev’s Inequality for Riesz Potentials of Functions in Musielak–Orlicz–Morrey Spaces Over Non-doubling Metric Measure Spaces

2019 ◽  
Vol 63 (2) ◽  
pp. 287-303
Author(s):  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Variable Exponents ◽  
Metric Measure Spaces ◽  
Riesz Potentials ◽  
Sobolev’S Inequality ◽  
Double Phase ◽  
Measure Spaces

AbstractOur aim in this paper is to establish a generalization of Sobolev’s inequality for Riesz potentials $I_{\unicode[STIX]{x1D6FC}(\,\cdot \,),\unicode[STIX]{x1D70F}}f$ of order $\unicode[STIX]{x1D6FC}(\,\cdot \,)$ with $f\in L^{\unicode[STIX]{x1D6F7},\unicode[STIX]{x1D705},\unicode[STIX]{x1D703}}(X)$ over bounded non-doubling metric measure spaces. As a corollary we obtain Sobolev’s inequality for double phase functionals with variable exponents.

SOBOLEV’S INEQUALITY FOR MUSIELAK–ORLICZ–MORREY SPACES OVER METRIC MEASURE SPACES

2019 ◽  
pp. 1-15
Author(s):  
TAKAO OHNO ◽  
TETSU SHIMOMURA
Keyword(s):  
Morrey Spaces ◽  
Variable Exponents ◽  
Metric Measure Spaces ◽  
Riesz Potentials ◽  
Sobolev’S Inequality ◽  
Double Phase ◽  
Measure Spaces

Our aim in this paper is to establish a generalization of Sobolev’s inequality for Riesz potentials $J_{\unicode[STIX]{x1D6FC}(\cdot )}^{\unicode[STIX]{x1D70E}}f$ of functions $f$ in Musielak–Orlicz–Morrey spaces $L^{\unicode[STIX]{x1D6F7},\unicode[STIX]{x1D705}}(X)$ . As a corollary we obtain Sobolev’s inequality for double phase functionals with variable exponents.

On Trudinger-type Inequalities in Orlicz-Morrey Spaces of an Integral Form

2020 ◽  
pp. 1-16
Author(s):  
Ritva Hurri-Syrjänen ◽  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Integral Form ◽  
Morrey Spaces ◽  
Metric Measure Spaces ◽  
Riesz Potentials ◽  
Euclidean Case ◽  
Measure Spaces

Abstract We give Trudinger-type inequalities for Riesz potentials of functions in Orlicz-Morrey spaces of an integral form over non-doubling metric measure spaces. Our results are new even for the doubling metric measure setting. In particular, our results improve and extend the previous results in Morrey spaces of an integral form in the Euclidean case.

scholarly journals Generalized Bessel and Riesz Potentials on Metric Measure Spaces

2009 ◽  
Vol 30 (4) ◽  
pp. 315-340 ◽  
Author(s):  
J. Hu ◽  
M. Zähle
Keyword(s):  
Metric Measure Spaces ◽  
Riesz Potentials ◽  
Measure Spaces

Maximal and fractional integral operators on generalized Morrey spaces over metric measure spaces

2018 ◽  
Vol 291 (8-9) ◽  
pp. 1400-1417 ◽  
Author(s):  
Idha Sihwaningrum ◽  
Hendra Gunawan ◽  
Eiichi Nakai
Keyword(s):  
Fractional Integral ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Metric Measure Spaces ◽  
Fractional Integral Operators ◽  
Generalized Morrey Spaces ◽  
Measure Spaces

A remark on modified Morrey spaces on metric measure spaces

2018 ◽  
Vol 47 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Yoshihiro SAWANO ◽  
Tetsu SHIMOMURA ◽  
Hitoshi TANAKA}
Keyword(s):  
Morrey Spaces ◽  
Metric Measure Spaces ◽  
Measure Spaces
Sign in / Sign up

Export Citation Format

Share Document