Regularity of one-sided multilinear fractional maximal functions
type: Item
instance of: scholarly article
title: Regularity of one-sided multilinear fractional maximal functions
zbMATH Open document ID: 1416.42022
author: Feng Liu
author: Lei Xu
published in: Open Mathematics
publication date: 2019-03-29T00:00:00Z
review text: The authors introduce the so-called one-sided multilinear fractional maximal operators, which are extensions of the one-sided Hardy-Littlewood maximal operators (which can be seen as the special case of the ergodic maximal operator). The investigations of regularity properties of one-sided maximal operators began with \textit{H. Tanaka} [Bull. Aust. Math. Soc. 65, No. 2, 253--258 (2002; Zbl 0999.42013)], and further by \textit{F. Liu} and \textit{S. Mao} [Czech. Math. J. 67, No. 1, 219--234 (2017; Zbl 1458.42016)] as well as \textit{F. Liu} [Math. Slovaca 68, No. 5, 1097--1112 (2018; Zbl 1505.42024)]. The authors extend the earlier results to the multilinear case. The results are, however too complicated to be stated here.
reviewed by: József Sándor
Mathematics Subject Classification ID: 42B25
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 7045530
zbMATH Keywords: one-sided multilinear fractional maximal operators
zbMATH Keywords: Sobolev spaces
zbMATH Keywords: discrete maximal operators
zbMATH Keywords: bounded variation
zbMATH Keywords: continuity
MaRDI profile type: Publication
full work available at URL: math-2018-0129
OpenAlex ID: W2911515760
cites work: The Hardy-Littlewood maximal function of a Sobolev function
cites work: Q4214072
cites work: REGULARITY OF THE FRACTIONAL MAXIMAL FUNCTION
cites work: On the regularity of maximal operators
cites work: On the Regularity of the Multisublinear Maximal Functions
cites work: On the regularity of the one-sided Hardy-Littlewood maximal functions
cites work: Continuity of the maximal operator in Sobolev spaces
cites work: On the regularity of the Hardy-Littlewood maximal operator on subdomains of ℝn
cites work: Q4820894
cites work: A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function
cites work: Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities
cites work: A NOTE ON THE ENDPOINT REGULARITY OF THE HARDY–LITTLEWOOD MAXIMAL FUNCTIONS
cites work: On the variation of the Hardy-Littlewood maximal function
cites work: Derivative bounds for fractional maximal functions
cites work: Endpoint Regularity of Multisublinear Fractional Maximal Functions
cites work: Endpoint Sobolev and BV continuity for maximal operators
cites work: A NOTE ON MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES OF REVOLUTION
cites work: On the variation of maximal operators of convolution type
cites work: A new integrable symplectic map by the binary nonlinearization to the super AKNS system
cites work: Continuity and approximate differentiability of multisublinear fractional maximal functions
cites work: A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy
cites work: Boundedness and continuity of maximal singular integrals and maximal functions on Triebel-Lizorkin spaces
cites work: On approximate differentiability of the maximal function
cites work: Rough maximal singular integral and maximal operators supported by subvarieties on Triebel-Lizorkin spaces
cites work: On the regularity of maximal operators supported by submanifolds
cites work: Weighted Norm Inequalities for the Riemann-Liouville and Weyl Fractional Integral Operators
cites work: On the regularity of one-sided fractional maximal functions
cites work: On a discrete version of Tanaka’s theorem for maximal functions
cites work: A REMARK ON THE REGULARITY OF THE DISCRETE MAXIMAL OPERATOR
cites work: On the endpoint regularity of discrete maximal operators
cites work: SHARP INEQUALITIES FOR THE VARIATION OF THE DISCRETE MAXIMAL FUNCTION
cites work: The frequency function and its connections to the Lebesgue points and the Hardy–Littlewood maximal function
cites work: Regularity of discrete multisublinear fractional maximal functions
cites work: A note on the endpoint regularity of the discrete maximal operator
cites work: A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
Wikidata QID: Q128465450
DOI: 10.1515/MATH-2018-0129
description: scientific article; zbMATH DE number 7045530