Weak estimates for the maximal and Riesz potential operators in non-homogeneous central Herz-Morrey spaces

2018 ◽  
Vol 64 (9) ◽  
pp. 1437-1456 ◽  
Author(s):  
Yoshihiro Mizuta ◽  
Takao Ohno ◽  
Tetsu Shimomura
Keyword(s):  
Riesz Potential ◽  
Morrey Spaces ◽  
Potential Operators

scholarly journals Applications of Littlewood-Paley Theory forB˙σ-Morrey Spaces to the Boundedness of Integral Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Yasuo Komori-Furuya ◽  
Katsuo Matsuoka ◽  
Eiichi Nakai ◽  
Yoshihiro Sawano
Keyword(s):  
Riesz Potential ◽  
Integral Operators ◽  
Morrey Spaces ◽  
Lipschitz Spaces ◽  
Potential Operators

The boundedness of the various operators onB˙σ-Morrey spaces is considered in the framework of the Littlewood-Paley decompositions. First, the Littlewood-Paley characterization ofB˙σ-Morrey-Campanato spaces is established. As an application, the boundedness of Riesz potential operators is revisted. Also, a characterization ofB˙σ-Lipschitz spaces is obtained: and, as an application, the boundedness of Riesz potential operators onB˙σ-Lipschitz spaces is discussed.

A class of subspaces of Morrey spaces and norm inequalities on Riesz potential operators

2014 ◽  
Vol 26 (5-6) ◽  
pp. 717-739
Author(s):  
Ibrahim Fofana ◽  
Falé Roland Faléa ◽  
Bérenger Akon Kpata
Keyword(s):  
Riesz Potential ◽  
Morrey Spaces ◽  
Norm Inequalities ◽  
Potential Operators

scholarly journals Weighted Hardy and Potential Operators in Morrey Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Natasha Samko
Keyword(s):  
Riesz Potential ◽  
Sufficient Conditions ◽  
Morrey Spaces ◽  
Potential Operator ◽  
Potential Operators ◽  
Riesz Potential Operator ◽  
Power Weights ◽  
The One ◽  
Necessary And Sufficient ◽  
Hardy Type Operators

We study the weightedp→q-boundedness of Hardy-type operators in Morrey spacesℒp,λ(ℝn) (orℒp,λ(ℝ+1) in the one-dimensional case) for a class of almost monotonic weights. The obtained results are applied to a similar weightedp→q-boundedness of the Riesz potential operator. The conditions on weights, both for the Hardy and potential operators, are necessary and sufficient in the case of power weights. In the case of more general weights, we provide separately necessary and sufficient conditions in terms of Matuszewska-Orlicz indices of weights.

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 } .

scholarly journals Riesz potential on the Heisenberg group and modified Morrey spaces

2012 ◽  
Vol 20 (1) ◽  
pp. 189-212
Author(s):  
Vagif S. Guliyev ◽  
Yagub Y. Mammadov
Keyword(s):  
Heisenberg Group ◽  
Fractional Integral ◽  
Morrey Space ◽  
Riesz Potential ◽  
Morrey Spaces ◽  
Potential Operator ◽  
Group Setting ◽  
Riesz Potential Operator ◽  
Homogeneous Dimension ◽  
Limiting Case

Abstract In this paper we study the fractional maximal operator Mα, 0 ≤ α < Q and the Riesz potential operator ℑα, 0 < α < Q on the Heisenberg group in the modified Morrey spaces L͂p,λ(ℍn), where Q = 2n + 2 is the homogeneous dimension on ℍn. We prove that the operators Mα and ℑα are bounded from the modified Morrey space L͂1,λ(ℍn) to the weak modified Morrey space WL͂q,λ(ℍn) if and only if, α/Q ≤ 1 - 1/q ≤ α/(Q - λ) and from L͂p,λ(ℍn) to L͂q,λ(ℍn) if and only if, α/Q ≤ 1/p - 1/q ≤ α/(Q - λ).In the limiting case we prove that the operator Mα is bounded from L͂p,λ(ℍn) to L∞(ℍn) and the modified fractional integral operator Ĩα is bounded from L͂p,λ(ℍn) to BMO(ℍn).As applications of the properties of the fundamental solution of sub-Laplacian Ը on ℍn, we prove two Sobolev-Stein embedding theorems on modified Morrey and Besov-modified Morrey spaces in the Heisenberg group setting. As an another application, we prove the boundedness of ℑα from the Besov-modified Morrey spaces BL͂spθ,λ(ℍn) to BL͂spθ,λ(ℍn).

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