Hardy-littlewood maximal operator

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August undefined, 2024

WebThen the Hardy-Littlewood maximal operator is bounded on Lp(x)(). Condition (1.4) is the natural analogue of (1.2) at in nity. It implies that there is some

The Boundedness of the Hardy-Littlewood Maximal …

WebApr 1, 2024 · For 1 < p < ∞ and M the centered Hardy–Littlewood maximal operator on R, we consider whether there is some ε = ε (p) > 0 such that M f p ≥ (1 + ε) f p. … WebConsider the maximal operator defined by 1 Z MD (f, g)(x) = sup F (y, z) dydz (11) h,w Px,l,w Px,l,w 3 If M1 is the 1−dimensional Hardy Littlewood operator and MV denotes the operator in R2 acting on the vertical variable z only, given by w 1 Z MV F (y, z) = sup F (y, z + s) ds (12) w 2w −w we have, observing that for f, g ≥ 0, MV F ... college application tracker excel

A Weak Type Vector-Valued Inequality for the Modified Hardy–Littlewood …

WebIn this paper we consider the Hardy-Littlewood maximal operator, (1.1) Mf(x) = sup B3x 1 jBj Z B\ jf(y)jdy; where the supremum is taken over all balls B which contain x and for which jB \ WebFeb 18, 2024 · The dyadic maximal operator has enjoyed a bit less attention than its continuous counterparts, such as the centered and the uncentered Hardy–Littlewood maximal operator. The dyadic maximal operator is different in the sense that formula ( 1.2 ) only holds for $\alpha =0$ , $p=1$ and only in the variation sense, for which formula ( … WebThis is motivated by matrix valued Harmonic Analysis (operator weighted norm inequalities, operator Hilbert transform), as well as, by the recent development of noncommutative martingale inequalities. ... (1 < P < infinity). (iv) The noncommutative Hardy-Littlewood maximal inequality. (v) A description of BMO as an intersection of two dyadic ... dr panoff miami

What is the $L^p$-norm of the (uncentered) Hardy-Littlewood maximal ...

The Hardy Littlewood Maximal Operator on Variable L P Spaces

WebAug 24, 2024 · The Hardy-Littlewood maximal functions play an important role in harmonic analysis. Their boundness and sharp bounds are important since a variety of operators are controlled by maximal functions. The and boundness of Hardy-Littlewood maximal functions are well-known [1–5]. However, sharp bounds are very hard to obtain. For a … WebFeb 5, 2016 · Dimension free bounds for the Hardy--Littlewood maximal operator associated to convex sets. Luc Deleaval, Olivier Guédon, Bernard Maurey. This survey is … dr pankratz marshfield clinicWebMar 24, 2024 · Title: Dimension free bounds for the vector-valued Hardy-Littlewood maximal operator Authors: Luc Deleaval (LAMA), Christoph Kriegler (LMBP) Download … dr panorea hudson

"WebThe sharp estimates of the m-linear p-adic Hardy and Hardy-Littlewood-Polya operators on Lebesgue spaces with power weights are obtained in this paper. 展开机译：本文获得了用功率重量的Lebesgue空间上的M-Linear P-ADIC硬质和硬性小木 - Polya算子的急剧估计。 " - Hardy-littlewood maximal operator

Hardy-littlewood maximal operator

WebJul 1, 1995 · @article{Prez1995OnSC, title={On Sufficient Conditions for the Boundedness of the Hardy–Littlewood Maximal Operator between Weighted Lp‐Spaces with Different Weights}, author={Carlos P{\'e}rez}, journal={Proceedings of The London Mathematical Society}, year={1995}, pages={135-157} } C. Pérez; Published 1 July 1995; Mathematics WebNov 9, 2024 · The aim of this paper is to prove the weak type vector-valued inequality for the modified Hardy– Littlewood maximal operator for general Radon measure on ℝn. Earlier, the strong type vector ...

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WebJan 1, 2004 · When the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue spaces, many results in classic harmonic analysis and function theory are also … WebOct 21, 2024 · The operator M is said to be the Hardy–Littlewood maximal operator. Definition 2.2. A weight w is a locally integrable and positive function defined on $\mathbb{R}^{n}$. Furthermore, a weight w is said to be an $A_{1}$ weight if

WebHere M is the Hardy–Littlewood maximal operator in ℝ n, Hα is the α-dimensional Hausdorff content, and the integrals are taken in the Choquet sense. The Choquet integral of ϕ [ges ]0 with respect to a set function C is defined by formula here Precise definitions of M and Hα will be given below. WebApr 23, 2024 · For a function , the Hardy–Littlewood maximal operator on G is defined as. If G has vertices, the maximal operator can be rewritten by. Over the last several years …

WebMay 7, 2024 · The Hardy–Littlewood maximal function is defined by M (f) (x)=\sup_ {B}\frac {1} { \vert B \vert } \int _ {B} \bigl\vert f (y) \bigr\vert \, {d}y, where the supremum is taken over all balls B containing x. We say that T is a singular integral operator if there exists a function K which satisfies the following conditions: WebHardy-Littlewood maximal operator, the main tool in our proof will be the following spherical maximal operator MS, initially deﬁned for f∈ S(Rd) by MSf(x) = sup r>0 Z Sd−1 f(x−ry)dσ(y) , x∈ Rd, where dσdenotes the normalized Haar measure on Sd−1, and for which we will prove in particular the following vector-valued estimates ...

WebJan 1, 2004 · In particular, after the boundedness of the Hardy-Littlewood maximal operator has been proved in [6,10, 28], Lebesgue spaces and various other function spaces arising in analysis and PDE, such as...

In their original paper, G.H. Hardy and J.E. Littlewood explained their maximal inequality in the language of cricket averages. Given a function f defined on R , the uncentred Hardy–Littlewood maximal function Mf of f is defined as at each x in R . Here, the supremum is taken over balls B in R which contain the point x and B denotes the measure of B (in this case a multiple of the radius of the ball raised to the power n). … college application topicsWeb1. The Hardy-Littlewood maximal inequality Let us work in Euclidean space Rd with Lebesgue measure; we write E instead of µ(E) for the Lebesgue measure of a set E. … college application week 2023WebHardy-Littlewood maximal operator on L^p (x) (ℝ) A. Nekvinda Published 2004 Mathematics Mathematical Inequalities & Applications View via Publisher files.ele … dr pan orthopaedicWebOct 3, 2014 · 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+ … college app stat crosswordWeb1.2. The Hardy-Littlewood Maximal Operator and the Strong Maximal Operator The Hardy-Littlewood maximal operator and its variants, along with so-called square functions and singular integrals, form the central objects of study in har-monic analysis [12]. It is de ned as follows. De nition. Let fbe a locally integrable function on Rd. The ... dr pan ortho virginiaWebHardy-Littlewood maximal operator on L^p (x) (ℝ) A. Nekvinda Published 2004 Mathematics Mathematical Inequalities & Applications View via Publisher files.ele-math.com Save to Library Create Alert Cite 258 Citations Citation Type More Filters Wavelet characterization of Sobolev spaces with variable exponent M. Izuki Mathematics 2011 college apply bdWebJan 20, 2016 · It is well known that the Hardy-Littlewood maximal function plays an important role in many parts of analysis. It is a classical mean operator, and it is … college applications with no application fee