New Proofs of Weighted Inequalities for the One-Sided Hardy-Littlewood Maximal Functions

1993 ◽  
Vol 117 (3) ◽  
pp. 691 ◽  
Author(s):  
F. J. Martin-Reyes
Keyword(s):  
Maximal Functions ◽  
Weighted Inequalities ◽  
The One

On the regularity of one-sided fractional maximal functions

2018 ◽  
Vol 68 (5) ◽  
pp. 1097-1112 ◽  
Author(s):  
Feng Liu
Keyword(s):  
Bounded Variation ◽  
Maximal Functions ◽  
Continuous Case ◽  
Discrete Case ◽  
Maximal Operators ◽  
Functions Of Bounded Variation ◽  
Sharp Bounds ◽  
Regularity Properties ◽  
Natural Extensions ◽  
The One

Abstract In this paper we investigate the regularity properties of one-sided fractional maximal functions, both in continuous case and in discrete case. We prove that the one-sided fractional maximal operators $ \mathcal{M}_{\beta}^{+} $ and $ \mathcal{M}_{\beta}^{-} $ map $ W^{1,p}(\mathbb{R}) $ into $ W^{1,q}(\mathbb{R}) $ with 1 <p <∞, 0≤β<1/p and q=p/(1-pβ), boundedly and continuously. In addition, we also obtain the sharp bounds and continuity for the discrete one-sided fractional maximal operators $ M_{\beta}^{+} $ and $ M_{\beta}^{-} $ from $ \ell^{1}(\mathbb{Z}) $ to $ {\rm BV}(\mathbb{Z}) $. Here $ {\rm BV}(\mathbb{Z}) $ denotes the set of all functions of bounded variation defined on ℤ. The results we obtained represent significant and natural extensions of what was known previously.

Weighted inequalities for the one-sided geometric maximal operators

2011 ◽  
Vol 284 (11-12) ◽  
pp. 1515-1522 ◽  
Author(s):  
Pedro Ortega Salvador ◽  
Consuelo Ramírez Torreblanca
Keyword(s):  
Maximal Operators ◽  
Weighted Inequalities ◽  
The One

The one-sided dyadic Hardy—Littlewood maximal operator

2014 ◽  
Vol 144 (5) ◽  
pp. 991-1006
Author(s):  
María Lorente ◽  
Francisco J. Martín-Reyes
Keyword(s):  
Maximal Operator ◽  
Weighted Inequalities ◽  
The One ◽  
Littlewood Maximal Operator

The main aim of this paper is to introduce an appropriate dyadic one-sided maximal operator , smaller than the one-sided Hardy–Littlewood maximal operator M+ but such that it controls M+ in a similar way to how the usual dyadic maximal operator controls the Hardy-Littlewood maximal operator. We characterize the weighted inequalities for this dyadic one-sided maximal operator.

scholarly journals Regularity of Commutators of the One-Sided Hardy-Littlewood Maximal Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Daiqing Zhang
Keyword(s):  
Sobolev Spaces ◽  
Maximal Functions ◽  
Regularity Properties ◽  
Discrete Analogues ◽  
The One ◽  
Derivatives Of

In this paper, the regularity properties of two classes of commutators of the one-sided Hardy-Littlewood maximal functions and their fractional variants are investigated. Some new bounds for the derivatives of the above commutators and the boundedness and continuity for the above commutators on the Sobolev spaces will be presented. The corresponding results for the discrete analogues are also considered.

scholarly journals On the regularity of the one-sided Hardy-Littlewood maximal functions

2017 ◽  
Vol 67 (1) ◽  
pp. 219-234 ◽  
Author(s):  
Feng Liu ◽  
Suzhen Mao
Keyword(s):  
Maximal Functions ◽  
The One

Weighted Inequalities for One-Sided Maximal Functions

1990 ◽  
Vol 319 (2) ◽  
pp. 517 ◽  
Author(s):  
F. J. Martin-Reyes ◽  
P. Ortega Salvador ◽  
A. De La Torre
Keyword(s):  
Maximal Functions ◽  
Weighted Inequalities
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