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.

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 Sharp integral estimates for the fractional maximal function and interpolation

2006 ◽  
Vol 44 (2) ◽  
pp. 309-326 ◽  
Author(s):  
Natan Kruglyak ◽  
Evgeny A. Kuznetsov
Keyword(s):  
Maximal Function ◽  
Fractional Maximal Function

scholarly journals Sharp Weighted Bounds for Multilinear Fractional Type Operators Associated with Bergman Projection

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Juan Zhang ◽  
Senhua Lan ◽  
Qingying Xue
Keyword(s):  
Maximal Function ◽  
Bergman Projection ◽  
Weighted Estimates ◽  
Fractional Maximal Function ◽  
Multiple Weights ◽  
Fractional Type

We first introduce the multiple weights which are suitable for the study of Bergman type operators. Then, we give the sharp weighted estimates for multilinear fractional Bergman operators and fractional maximal function.

REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION

2003 ◽  
Vol 35 (04) ◽  
pp. 529-535 ◽  
Author(s):  
JUHA KINNUNEN ◽  
EERO SAKSMAN
Keyword(s):  
Maximal Function ◽  
Fractional Maximal Function

scholarly journals Endpoint Sobolev Continuity of the Fractional Maximal Function in Higher Dimensions

2019 ◽  
Author(s):  
David Beltran ◽  
José Madrid
Keyword(s):  
Maximal Function ◽  
Maximal Operator ◽  
Higher Dimensions ◽  
Input Space ◽  
Fractional Maximal Operator ◽  
Fractional Maximal Function

Abstract We establish continuity mapping properties of the noncentered fractional maximal operator $M_{\beta }$ in the endpoint input space $W^{1,1}({\mathbb R}^d)$ for $d \geq 2$ in the cases for which its boundedness is known. More precisely, we prove that for $q=d/(d-\beta )$ the map $f \mapsto |\nabla M_\beta f|$ is continuous from $W^{1,1}({\mathbb R}^d)$ to $L^{q}({\mathbb R}^d)$ for $ 0 < \beta < 1$ if $f$ is radial and for $1 \leq \beta < d$ for general $f$. The results for $1\leq \beta < d$ extend to the centered counterpart $M_\beta ^c$. Moreover, if $d=1$, we show that the conjectured boundedness of that map for $M_\beta ^c$ implies its continuity.

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