Equivalence of norms of Riesz potential and fractional maximal function in generalized Morrey spaces

2010 ◽  
Vol 63 (1) ◽  
pp. 11-28 ◽  
Author(s):  
Amiran Gogatishvili ◽  
Rza Mustafayev
Keyword(s):  
Maximal Function ◽  
Riesz Potential ◽  
Morrey Spaces ◽  
Generalized Morrey Spaces ◽  
Fractional Maximal Function

An extension of the Muckenhoupt–Wheeden theorem to generalized weighted Morrey spaces

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Rza Mustafayev ◽  
Abdulhamit Kucukaslan
Keyword(s):  
Maximal Function ◽  
Riesz Potential ◽  
Morrey Spaces ◽  
Fractional Maximal Function ◽  
Weighted Morrey Spaces

AbstractIn this paper, we find the condition on a function ω and a weight v which ensures the equivalency of norms of the Riesz potential and the fractional maximal function in generalized weighted Morrey spaces {{\mathcal{M}}_{p,\omega}({\mathbb{R}}^{n},v)} and generalized weighted central Morrey spaces {\dot{\mathcal{M}}_{p,\omega}({\mathbb{R}}^{n},v)}, when v belongs to the Muckenhoupt {A_{\infty}}-class.

scholarly journals Some estimates for the commutators of multilinear maximal function on Morrey-type space

2021 ◽  
Vol 19 (1) ◽  
pp. 515-530
Author(s):  
Xiao Yu ◽  
Pu Zhang ◽  
Hongliang Li
Keyword(s):  
Maximal Function ◽  
Morrey Space ◽  
Morrey Spaces ◽  
Bounded Mean Oscillation ◽  
Generalized Morrey Spaces ◽  
Type Space ◽  
Bmo Function ◽  
Mean Oscillation ◽  
Multilinear Maximal Function ◽  
Equivalent Conditions

Abstract In this paper, we study the equivalent conditions for the boundedness of the commutators generated by the multilinear maximal function and the bounded mean oscillation (BMO) function on Morrey space. Moreover, the endpoint estimate for such operators on generalized Morrey spaces is also given.

Commutator of Riesz potential in p-adic generalized Morrey spaces

2018 ◽  
Vol 13 (3) ◽  
pp. 633-645 ◽  
Author(s):  
Huixia Mo ◽  
Xiaojuan Wang ◽  
Ruiqing Ma
Keyword(s):  
Riesz Potential ◽  
Morrey Spaces ◽  
Generalized Morrey Spaces

Riesz potential in generalized Morrey spaces on the Heisenberg group

2013 ◽  
Vol 189 (3) ◽  
pp. 365-382 ◽  
Author(s):  
V. S. Guliyev ◽  
A. Eroglu ◽  
Y. Y. Mammadov
Keyword(s):  
Heisenberg Group ◽  
Riesz Potential ◽  
Morrey Spaces ◽  
Generalized Morrey Spaces

scholarly journals Riesz Potential and Fractional Maximal Function

2021 ◽  
Vol 6 ◽  
pp. 137-141
Author(s):  
Santosh Ghimire
Keyword(s):  
Maximal Function ◽  
Riesz Potential ◽  
Fractional Maximal Function ◽  
The Space Lp

In this article, we begin with Riesz potential. We then discuss some properties of the Riesz potential. Finally we discuss a relation of  Riesz Potential with fractional maximal function in the sense that fractional maximal function can be controlled by Riesz potential and the fractional  maximal function maps  the space Lp to Lq whenever the Riesz potential does.

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