Boundedness of Maximal Operators and Sobolev’s Inequality on Non-Homogeneous Central Musielak–Orlicz–Morrey Spaces

2016 ◽  
Vol 13 (5) ◽  
pp. 3341-3357
Author(s):  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Maximal Operators ◽  
Sobolev’S Inequality

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.

scholarly journals A Gradient Estimate Related Fractional Maximal Operators for a $p$-Laplace Problem in Morrey Spaces

2021 ◽  
Vol -1 (-1) ◽  
Author(s):  
Thanh-Nhan Nguyen ◽  
Minh-Phuong Tran ◽  
Cao-Kha Doan ◽  
Van-Nghia Vo
Keyword(s):  
Morrey Spaces ◽  
Gradient Estimate ◽  
Maximal Operators ◽  
Laplace Problem

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.

Equivalence of operator norm for Hardy-Littlewood maximal operators and their truncated operators on Morrey spaces

2020 ◽  
Vol 15 (1) ◽  
pp. 215-223
Author(s):  
Xingsong Zhang ◽  
Mingquan Wei ◽  
Dunyan Yan ◽  
Qianjun He
Keyword(s):  
Morrey Spaces ◽  
Operator Norm ◽  
Maximal Operators
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