2024 Hardy-littlewood maximal operator

Hardy-littlewood maximal operator

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August undefined, 2024

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 ... 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). …

On the regularity of the Hardy-Littlewood maximal operator on ...

WebJan 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 … jeep 96th st indianapolis

Hardy-Littlewood maximal operator on Lp(x)(Rn) - ResearchGate

WebJan 20, 2016 · When p=1, we also find that the weak (1,1) norm of the truncated centered Hardy-Littlewood maximal operator M^ {c}_ {\gamma} equals the weak (1,1) norm of … WebHardy-Littlewood maximal operator on L^p (x) (ℝ) A. Nekvinda Published 2004 Mathematics Mathematical Inequalities & Applications View via Publisher files.ele … Web1.2. 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 ... jeep 97 tj

On Sufficient Conditions for the Boundedness of the Hardy–Littlewood …

Hardy-Littlewood maximal operator on L^p(x) (ℝ) - Semantic …

In mathematics, the Hardy–Littlewood maximal operator M is a significant non-linear operator used in real analysis and harmonic analysis. The operator takes a locally integrable function f : R → C and returns another function Mf. For any point x ∈ R , the function Mf returns the maximum of a set of reals, namely the set … See more This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from the L (R ) to itself for p > 1. That is, if f ∈ L (R ) then the maximal function Mf is weak L -bounded and Mf ∈ L (R ). Before stating … See more It is still unknown what the smallest constants Cp,d and Cd are in the above inequalities. However, a result of Elias Stein about spherical maximal functions can be used to … See more While there are several proofs of this theorem, a common one is given below: For p = ∞, the inequality is trivial (since the average of a function is no larger than its essential supremum). … See more • Rising sun lemma See more WebA pointwise estimate involving Hardy-Littlewood maximal operator. 3. Hardy-Littlewood maximal function of a probability density. 1. A question about Hardy-Littlewood maximal function and a characterization of measurable sets. 2. Is the norm of the Hardy-Littlewood maximal operator bounded? 1. lagu daerah dari jakartaWebMar 24, 2024 · Title: Dimension free bounds for the vector-valued Hardy-Littlewood maximal operator Authors: Luc Deleaval (LAMA), Christoph Kriegler (LMBP) Download … jeep 98

"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 " - Hardy-littlewood maximal operator

Hardy-littlewood maximal operator

An elementary approach to certain bilinear estimates

WebJun 2, 2024 · The Hardy–Littlewood maximal operator plays an important role in harmonic analysis, especially in the theory of differentiation of functions. A fundamental important problem for maximal operators is to obtain certain regularity problems such as weak-type inequalities or \(L^p\)-boundedness. WebJan 12, 2010 · We establish the continuity of the Hardy-Littlewood maximal operator on W 1, p (Ω), where Ω ⊂ ℝ n is an arbitrary subdomain and 1 < p < ∞. Moreover, …

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WebOct 1, 2006 · We will study the Hardy–Littlewood maximal function of a τ-measurable operator T .More precisely, letMbe a semi-finite von Neumann algebra with a normal … Web1. 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. …

WebThis is a corollary of the Hardy–Littlewood maximal inequality. Hardy–Littlewood maximal inequality. This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from the L p (R d) to itself for p > 1. That is, if f ∈ L p (R d) then the maximal function Mf is weak L 1-bounded and Mf ∈ L p (R d). 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 ...

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 … 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 \

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. …

WebHardy-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 jeep 98 4x4WebThe aim of this paper is to prove the boundedness of the Hardy-Littlewood maximal operator on weighted Morrey spaces and multilinear maximal operator on multiple weighted Morrey spaces. In particular, the result includes the Komori-Shirai theorem and the Iida-Sato-Sawano-Tanaka theorem for the Hardy-Littlewood maximal operator and … jeep 974WebFeb 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 ( … lagu daerah dari kalimantan selatanWebJul 22, 2024 · Download PDF Abstract: We give necessary and sufficient conditions for the boundedness of generalized fractional integral and maximal operators on Orlicz-Morrey and weak Orlicz-Morrey spaces. To do this we prove the weak-weak type modular inequality of the Hardy-Littlewood maximal operator with respect to the Young function. jeep 97 wranglerWebThen 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 jeep 98 xjWebNov 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 ... lagu daerah dari papuaWebOct 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+ … jeep9at