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.

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.

scholarly journals On weighted estimates for Stein's maximal function

1996 ◽  
Vol 54 (1) ◽  
pp. 35-39 ◽  
Author(s):  
Hendra Gunawan
Keyword(s):  
Maximal Function ◽  
Unit Sphere ◽  
Surface Measure ◽  
Weighted Estimates ◽  
Mellin Transformation ◽  
Transformation Approach ◽  
Image Position

Let φ denote the normalised surface measure on the unit sphere Sn−1. We shall be interested in the weighted Lp estimate for Stein's maximal function Mφf, namelywhere w is an Ap weight, especially for 1 < p ≤ 2. Using the Mellin transformation approach, we prove that the estimate holds for every weight wδ where w ∈ Ap and 0 ≤ δ < (p(n − 1) − n)/(n(p − 1)), for n ≥ 3 and n/(n − 1) < p ≤ 2.

scholarly journals vector-valued singular integrals and maximal functions on spaces of homogeneous type

2009 ◽  
Vol 104 (2) ◽  
pp. 296 ◽  
Author(s):  
Loukas Grafakos ◽  
Liguang Liu ◽  
Dachun Yang
Keyword(s):  
Singular Integral ◽  
Maximal Function ◽  
Singular Integrals ◽  
Maximal Functions ◽  
Integral Theory ◽  
Homogeneous Type ◽  
Spaces Of Homogeneous Type ◽  
Vector Valued

The Fefferman-Stein vector-valued maximal function inequality is proved for spaces of homogeneous type. The approach taken here is based on the theory of vector-valued Calderón-Zygmund singular integral theory in this context, which is appropriately developed.

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.

scholarly journals Maximal functions and transference for groups of operators

2000 ◽  
Vol 43 (1) ◽  
pp. 57-71 ◽  
Author(s):  
Gordon Blower
Keyword(s):  
Banach Spaces ◽  
Laplace Operator ◽  
Maximal Function ◽  
Maximal Functions ◽  
Abstract Version ◽  
The Laplace Operator

AbstractLet Δ be the Laplace operator on ℝd and 1 < δ < 2. Using transference methods we show that, for max {q, q/(q – 1)} < 4d/(2d + 1 – δ), the maximal function for the Schrödinger group is in Lq, for f ∈ Lq with Δδ/2f ∈Lq. We obtain a similar result for the Airy group exp it Δ3/2. An abstract version of these results is obtained for bounded C0-groups eitL on subspaces of Lp spaces. Certain results extend to maximal functions defined for functions with values in U M D Banach spaces.

scholarly journals SHARP INEQUALITIES FOR THE VARIATION OF THE DISCRETE MAXIMAL FUNCTION

2016 ◽  
Vol 95 (1) ◽  
pp. 94-107 ◽  
Author(s):  
JOSÉ MADRID
Keyword(s):  
Maximal Function ◽  
Maximal Functions ◽  
Discrete Version ◽  
Optimal Bounds

In this paper we establish new optimal bounds for the derivative of some discrete maximal functions, in both the centred and uncentred versions. In particular, we solve a question originally posed by Bober et al. [‘On a discrete version of Tanaka’s theorem for maximal functions’, Proc. Amer. Math. Soc.140 (2012), 1669–1680].

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.

BOUNDEDNESS OF MAXIMAL FUNCTIONS ON NONDOUBLING PARABOLIC MANIFOLDS WITH ENDS

2020 ◽  
pp. 1-25
Author(s):  
HONG CHUONG DOAN
Keyword(s):  
Heat Kernel ◽  
Maximal Function ◽  
Upper Bound ◽  
Nonnegative Integer ◽  
Weak Type ◽  
Adjoint Operator ◽  
Beltrami Operator ◽  
Maximal Functions ◽  
Heat Semigroup ◽  
Doubling Condition

Let $M$ be a nondoubling parabolic manifold with ends. First, this paper investigates the boundedness of the maximal function associated with the heat semigroup ${\mathcal{M}}_{\unicode[STIX]{x1D6E5}}f(x):=\sup _{t>0}|e^{-t\unicode[STIX]{x1D6E5}}f(x)|$ where $\unicode[STIX]{x1D6E5}$ is the Laplace–Beltrami operator acting on $M$ . Then, by combining the subordination formula with the previous result, we obtain the weak type $(1,1)$ and $L^{p}$ boundedness of the maximal function ${\mathcal{M}}_{\sqrt{L}}^{k}f(x):=\sup _{t>0}|(t\sqrt{L})^{k}e^{-t\sqrt{L}}f(x)|$ on $L^{p}(M)$ for $1<p\leq \infty$ where $k$ is a nonnegative integer and $L$ is a nonnegative self-adjoint operator satisfying a suitable heat kernel upper bound. An interesting thing about the results is the lack of both doubling condition of $M$ and the smoothness of the operators’ kernels.

The Riesz–Herz equivalence for capacitary maximal functions on metric measure spaces

2016 ◽  
Vol 7 (2) ◽  
Author(s):  
Pilar Silvestre
Keyword(s):  
Maximal Function ◽  
Maximal Functions ◽  
Metric Measure Spaces ◽  
Measure Spaces

AbstractWe prove a Riesz–Herz estimate for the maximal function

scholarly journals Maximal Function Characterizations of Hardy Spaces on Rn with Pointwise Variable Anisotropy

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3246
Author(s):  
Aiting Wang ◽  
Wenhua Wang ◽  
Baode Li
Keyword(s):  
Maximal Function ◽  
Hardy Spaces ◽  
Full Range ◽  
Real Variable ◽  
Maximal Functions ◽  
High Anisotropy ◽  
Multi Level ◽  
Point To Point ◽  
Variable Anisotropy

In 2011, Dekel et al. developed highly geometric Hardy spaces Hp(Θ), for the full range 0<p≤1, which were constructed by continuous multi-level ellipsoid covers Θ of Rn with high anisotropy in the sense that the ellipsoids can rapidly change shape from point to point and from level to level. In this article, when the ellipsoids in Θ rapidly change shape from level to level, the authors further obtain some real-variable characterizations of Hp(Θ) in terms of the radial, the non-tangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy spaces of Bownik.

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