scholarly journals Sobolev embeddings for Riesz potentials of functions in Morrey spaces L^1,ν,β_1,β_2(R^n)

2014 ◽  
pp. 1399-1414
Author(s):  
Yoshihiro Mizuta ◽  
Tetsu Shimomura
Keyword(s):  
Morrey Spaces ◽  
Riesz Potentials ◽  
Sobolev Embeddings

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.

scholarly journals An elementary proof of Sobolev embeddings for Riesz potentials of functions in Morrey spaces $L^{1,\nu,\beta}(G)$

2008 ◽  
Vol 38 (3) ◽  
pp. 425-436 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Eiichi Nakai ◽  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Elementary Proof ◽  
Morrey Spaces ◽  
Riesz Potentials ◽  
Sobolev Embeddings

scholarly journals B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials on B-Morrey spaces

2020 ◽  
Vol 18 (1) ◽  
pp. 715-730
Author(s):  
Javanshir J. Hasanov ◽  
Rabil Ayazoglu ◽  
Simten Bayrakci
Keyword(s):  
Differential Operator ◽  
Singular Integral ◽  
Riesz Potential ◽  
Type Theorem ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Singular Integral Operators ◽  
Sobolev Type ◽  
Riesz Potentials ◽  
Bessel Differential Operator

Abstract In this article, we consider the Laplace-Bessel differential operator {\Delta }_{{B}_{k,n}}=\mathop{\sum }\limits_{i=1}^{k}\left(\frac{{\partial }^{2}}{\partial {x}_{i}^{2}}+\frac{{\gamma }_{i}}{{x}_{i}}\frac{\partial }{\partial {x}_{i}}\right)+\mathop{\sum }\limits_{i=k+1}^{n}\frac{{\partial }^{2}}{\partial {x}_{i}^{2}},{\gamma }_{1}\gt 0,\ldots ,{\gamma }_{k}\gt 0. Furthermore, we define B-maximal commutators, commutators of B-singular integral operators and B-Riesz potentials associated with the Laplace-Bessel differential operator. Moreover, we also obtain the boundedness of the B-maximal commutator {M}_{b,\gamma } and the commutator {[}b,{A}_{\gamma }] of the B-singular integral operator and Hardy-Littlewood-Sobolev-type theorem for the commutator {[}b,{I}_{\alpha ,\gamma }] of the B-Riesz potential on B-Morrey spaces {L}_{p,\lambda ,\gamma } , when b\in {\text{BMO}}_{\gamma } .

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