Weighted Lorentz Norm Inequalities for the One-Sided Hardy-Littlewood Maximal Functions and for the Maximal Ergodic Operator

1994 ◽  
Vol 46 (5) ◽  
pp. 1057-1072 ◽  
Author(s):  
P. Ortega Salvador
Keyword(s):  
Maximal Function ◽  
Maximal Operator ◽  
Measure Space ◽  
Maximal Functions ◽  
Norm Inequalities ◽  
Littlewood Maximal Function ◽  
Measure Preserving Transformation ◽  
The One ◽  
Image Position ◽  
Lorentz Norm

AbstractIn this paper we characterize weighted Lorentz norm inequalities for the one sided Hardy-Littlewood maximal functionSimilar questions are discussed for the maximal operator associated to an invertible measure preserving transformation of a measure space.

Weighted Lorentz norm inequalities for general maximal operators associated with certain families of Borel measures

1998 ◽  
Vol 128 (2) ◽  
pp. 403-424 ◽  
Author(s):  
María Dolores Sarrión Gavilán
Keyword(s):  
Maximal Operator ◽  
Maximal Operators ◽  
Weighted Inequalities ◽  
General Measure ◽  
Norm Inequalities ◽  
Fractional Maximal Operator ◽  
Borel Measures ◽  
The One ◽  
Littlewood Maximal Operator ◽  
Lorentz Norm

Given a certain family ℱ of positive Borel measures and γ ∈ [0, 1), we define a general onesided maximal operatorand we study weighted inequalities inLp,qspaces for these operators. Our results contain, as particular cases, the characterisation of weighted Lorentz norm inequalities for some well-known one-sided maximal operators such as the one-sided Hardy–Littlewood maximal operator associated with a general measure, the one-sided fractional maximal operatorand the maximal operatorassociated with the Cesèro-α averages.

scholarly journals Norm inequalities relating one-sided singular integrals and the one-sided maximal function

2000 ◽  
Vol 69 (3) ◽  
pp. 403-414 ◽  
Author(s):  
M. S. Riveros ◽  
A. de la Torre
Keyword(s):  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Norm Inequalities ◽  
Littlewood Maximal Function ◽  
The One

AbstractIn this paper we prove that if a weight w satisfies the condition, then the Lp(w) norm of a one-sided singular integral is bounded by the Lp(w) norm of the one-sided Hardy-Littlewood maximal function, for 1 < p < q < ∞.

Weighted Lacunary Maximal Functions on Curves

1995 ◽  
Vol 38 (3) ◽  
pp. 271-277
Author(s):  
Jong-Guk Bak
Keyword(s):  
Maximal Function ◽  
Maximal Functions ◽  
Image Position

AbstractLet γ(t) = (t, t2,..., tn) + a be a curve in Rn, where n ≥ 2 and a ∊ Rn. We prove LP-Lq estimates for the weighted lacunary maximal function, related to this curve, defined byIf n = 2 or 3 our results are (nearly) sharp.

scholarly journals A remark on the derivative of the one-dimensional Hardy-Littlewood maximal function

2002 ◽  
Vol 65 (2) ◽  
pp. 253-258 ◽  
Author(s):  
Hitoshi Tanaka
Keyword(s):  
Sobolev Space ◽  
Maximal Function ◽  
60Th Birthday ◽  
One Dimensional ◽  
Partial Derivatives ◽  
First Order ◽  
Littlewood Maximal Function ◽  
The One ◽  
Derivatives Of

Dedicated to Professor Kôzô Yabuta on the occasion of his 60th birthdayJ. Kinnunen proved that of P > 1, d ≤ 1 and f is a function in the Sobolev space W1,P(Rd), then the first order weak partial derivatives of the Hardy-Littlewood maximal function ℳf belong to LP(Rd). We shall show that, when d = 1, Kinnunen's result can be extended to the case where P = 1.

A note on the one-dimensional maximal function

1989 ◽  
Vol 111 (3-4) ◽  
pp. 325-328 ◽  
Author(s):  
Antonio Bernal
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Type Inequality ◽  
Best Constant ◽  
Weak Type Inequality ◽  
One Dimensional ◽  
Littlewood Maximal Function ◽  
The One

SynopsisIn this note, we consider the Hardy-Littlewood maximal function on R for arbitrary measures, as was done by Peter Sjögren in a previous paper. We determine the best constant for the weak type inequality.

The Weak Type (1, 1) Estimates of Maximal Functions on the Laguerre Hypergroup

2010 ◽  
Vol 53 (3) ◽  
pp. 491-502 ◽  
Author(s):  
Jizheng Huang ◽  
Liu Heping
Keyword(s):  
Maximal Function ◽  
Weak Type ◽  
Maximal Functions ◽  
Laguerre Hypergroup ◽  
Littlewood Maximal Function

AbstractIn this paper, we discuss various maximal functions on the Laguerre hypergroup K including the heat maximal function, the Poisson maximal function, and the Hardy–Littlewood maximal function which is consistent with the structure of hypergroup of K. We shall establish the weak type (1, 1) estimates for these maximal functions. The Lp estimates for p > 1 follow fromthe interpolation. Some applications are included.

Endpoint Regularity of Multisublinear Fractional Maximal Functions

2017 ◽  
Vol 60 (3) ◽  
pp. 586-603 ◽  
Author(s):  
Feng Liu ◽  
Huoxiong Wu
Keyword(s):  
Maximal Operator ◽  
Maximal Functions ◽  
Maximal Operators ◽  
One Dimensional ◽  
Regularity Properties ◽  
The One ◽  
Vector Valued Function ◽  
Vector Valued ◽  
Littlewood Maximal Operator

AbstractIn this paper we investigate the endpoint regularity properties of the multisublinear fractional maximal operators, which include the multisublinear Hardy–Littlewood maximal operator. We obtain some new bounds for the derivative of the one-dimensional multisublinear fractional maximal operators acting on the vector-valued function with all ƒ j being BV-functions.

On the Regularity of the Multisublinear Maximal Functions

2015 ◽  
Vol 58 (4) ◽  
pp. 808-817 ◽  
Author(s):  
Feng Liu ◽  
Huoxiong Wu
Keyword(s):  
Sobolev Spaces ◽  
Maximal Function ◽  
Maximal Operator ◽  
Maximal Functions ◽  
Partial Derivatives ◽  
First Order ◽  
Derivatives Of

AbstractThis paper is concerned with the study of the regularity for the multisublinear maximal operator. It is proved that the multisublinear maximal operator is bounded on first-order Sobolev spaces. Moreover, two key point-wise inequalities for the partial derivatives of the multisublinear maximal functions are established. As an application, the quasi-continuity on the multisublinear maximal function is also obtained.

On the Uniqueness of Maximal Functions

1996 ◽  
Vol 3 (1) ◽  
pp. 49-52
Author(s):  
L. Ephremidze
Keyword(s):  
Uniqueness Theorem ◽  
Maximal Operator ◽  
Maximal Functions ◽  
The One ◽  
The Uniqueness Theorem

Abstract The uniqueness theorem for the one-sided maximal operator has been proved.

Sign in / Sign up

Export Citation Format

Share Document