scholarly journals On the lack of dimension-free estimates in Lp for maximal functions associated to radial measures

2010 ◽  
Vol 140 (3) ◽  
pp. 541-552 ◽  
Author(s):  
Alberto Criado
Keyword(s):  
Gaussian Measure ◽  
Maximal Operator ◽  
Recent Article ◽  
Maximal Functions

In a recent article Aldaz proved that the weak L1 bounds for the centred maximal operator associated to finite radial measures cannot be taken independently with respect to the dimension. We show that the same result holds for the Lp bounds of such measures with decreasing densities, at least for small p near to one. We also give some concrete examples, including the Gaussian measure, where better estimates with respect to the general case are obtained.

scholarly journals Maximal functions associated with families of homogeneous curves: Lp bounds for P ≤ 2

2020 ◽  
Vol 63 (2) ◽  
pp. 398-412
Author(s):  
Shaoming Guo ◽  
Joris Roos ◽  
Andreas Seeger ◽  
Po-Lam Yung
Keyword(s):  
Hilbert Transform ◽  
Maximal Operator ◽  
Maximal Functions ◽  
Homogeneous Curves

AbstractLet M(u), H(u) be the maximal operator and Hilbert transform along the parabola (t, ut2). For U ⊂ (0, ∞) we consider Lp estimates for the maximal functions sup u∈U|M(u)f| and sup u∈U|H(u)f|, when 1 < p ≤ 2. The parabolas can be replaced by more general non-flat homogeneous curves.

scholarly journals Two weighted ineqalities for maximal functions related to Cesàro convergence

2003 ◽  
Vol 74 (1) ◽  
pp. 111-120
Author(s):  
A. L. Bernardis ◽  
F. J. Martín-Reyes
Keyword(s):  
Maximal Operator ◽  
Singular Integrals ◽  
Weak Type ◽  
Maximal Functions ◽  
Cesaro Convergence

AbstractWe characterize the pairs of weights (u, v) for which the maximal operator is of weak and restricted weak type (p, p) with respect to u(x)dx and v(x)dx. As a consequence we obtain analogous results for We apply the results to the study of the Cesàro-α convergence of singular integrals.

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.

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.

A REMARK ON THE REGULARITY OF THE DISCRETE MAXIMAL OPERATOR

2016 ◽  
Vol 95 (1) ◽  
pp. 108-120 ◽  
Author(s):  
FENG LIU
Keyword(s):  
Maximal Operator ◽  
Maximal Functions ◽  
Maximal Operators ◽  
Sharp Bounds ◽  
Regularity Properties

We study the regularity properties of several classes of discrete maximal operators acting on $\text{BV}(\mathbb{Z})$ functions or $\ell ^{1}(\mathbb{Z})$ functions. We establish sharp bounds and continuity for the derivative of these discrete maximal functions, in both the centred and uncentred versions. As an immediate consequence, we obtain sharp bounds and continuity for the discrete fractional maximal operators from $\ell ^{1}(\mathbb{Z})$ to $\text{BV}(\mathbb{Z})$.

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.

Variable exponent Herz type Besov and Triebel–Lizorkin spaces

2018 ◽  
Vol 25 (1) ◽  
pp. 135-148 ◽  
Author(s):  
Jingshi Xu ◽  
Xiaodi Yang
Keyword(s):  
Maximal Operator ◽  
Variable Exponent ◽  
Maximal Functions ◽  
Herz Spaces ◽  
Vector Valued ◽  
Littlewood Maximal Operator

AbstractWe establish the boundedness of the vector-valued Hardy–Littlewood maximal operator in variable exponent Herz spaces, which were introduced by Samko in [33]. We also introduce variable exponent Herz type Besov and Triebel–Lizorkin spaces and give characterizations of these new spaces by maximal functions.

scholarly journals Characterizations of variable martingale Hardy spaces via maximal functions

2021 ◽  
Vol 24 (2) ◽  
pp. 393-420
Author(s):  
Ferenc Weisz
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Lorentz Space ◽  
Maximal Operator ◽  
Variable Exponent ◽  
Continuity Condition ◽  
Maximal Functions ◽  
Maximal Operators ◽  
Special Cases ◽  
New Type

Abstract We introduce a new type of dyadic maximal operators and prove that under the log-Hölder continuity condition of the variable exponent p(⋅), it is bounded on L p(⋅) if 1 < p − ≤ p + ≤ ∞. Moreover, the space generated by the L p(⋅)-norm (resp. the L p(⋅), q -norm) of the maximal operator is equivalent to the Hardy space H p(⋅) (resp. to the Hardy-Lorentz space H p(⋅), q ). As special cases, our maximal operator contains the usual dyadic maximal operator and four other maximal operators investigated in the literature.

On the Integrability of Strong Maximal Functions Corresponding to Different Frames

1999 ◽  
Vol 6 (2) ◽  
pp. 149-168
Author(s):  
G. Oniani
Keyword(s):  
General Solution ◽  
Maximal Operator ◽  
Maximal Functions ◽  
Straight Lines

Abstract For the frame θ in , let B 2(θ)(𝑥) (𝑥 ∈ ) be a family of all 𝑛-dimensional rectangles containing 𝑥 and having edges parallel to the straight lines of θ, and let MB2(θ) be a maximal operator corresponding to B 2(θ). The main result of the paper is the following Theorem. For any function 𝑓 ∈ 𝐿 (1 + ln+ 𝐿)() (𝑛 ≥ 2) there exists a measure preserving and invertible mapping such that 1. {𝑥 : ω(𝑥) ≠ 𝑥} ⊂ supp 𝑓; 2. This theorem gives a general solution of M. de Guzmán's problem that was previously studied by various authors.

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