On the regularity of maximal operators

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August undefined, 2024

Web14 de abr. de 2024 · We extend the recently much-studied Hardy factorization theorems to the weight case. The key point of this paper is to establish the factorization theorems … Webmaximal function in the Sobolev space W1;p(), p > n=(n 1). We also raise many questions concerning boundedness of maximal operators in Sobolev spaces. 1. Introduction The theory of Sobolev spaces and the Hardy{Littlewood maximal function, one of the most important tools in analysis, have been developed a great deal for more than seven …

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WebRemark 3: Another interesting variant would be to consider the spherical maximal operator [3, 16] and its discrete analogue . The non-endpoint regularity of the continuous operator in Sobolev spaces was proved in and it would be interesting to investigate what happens in the endpoint case, both in the continuous and in the discrete settings. Web4 de out. de 2024 · For the developments related to endpoint regularity of maximal operators, we refer the reader to [ 1, 2, 3, 5 ], among others. It should be pointed out … green bay first assembly of god

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WebIt is used to characterize maximal regularity of periodic Cauchy problems. Keywords: Fourier multipliers; Besov spaces; periodic solutions; Cauchy problem; maximal regularity 2000 Mathematics subject classiﬁcation: Primary 47D06; 42A45 1. Introduction In a series of recent publications, operator-valued Fourier multiplier theorems on diverse Webthe maximal operator. While the Christ-Goldberg maximal operator MW was sufﬁcient to prove strong (p,p) bounds for singular integrals, it has the drawback that it maps a vector-valued function f~ to scalar-valued function M W f~. Therefore, it cannot be iterated, and so cannot be usedto constructa Rubiode Francia iterationoperator. Web10 de dez. de 2024 · This is an expository paper on the regularity theory of maximal operators, when these act on Sobolev and BV functions, with a special focus on some … green bay first assembly

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Web29 de mar. de 2024 · Several new pointwise estimates for the derivative of the local multilinear maximal function {\mathfrak {M}}_ {0,\Omega } and the fractional maximal … WebWe also investigate the almost everywhere and weak convergence under the action of the classical Hardy-Littlewood maximal operator, both in its global and local versions. Now on home page ads green bay first assembly of god churchWebHardy–Littlewood maximal inequality [ edit] This theorem of G. H. Hardy and J. E. Littlewood states that M is bounded as a sublinear operator from the Lp ( Rd) to itself for p > 1. That is, if f ∈ Lp ( Rd) then the maximal function Mf is weak L1 -bounded and Mf ∈ Lp ( Rd ). Before stating the theorem more precisely, for simplicity, let ... green bay fire station 8

"Web6 de set. de 2013 · Title: On the endpoint regularity of discrete maximal operators. ... We also prove the same result for the non-centered version of this discrete maximal operator. Subjects: Classical Analysis and ODEs (math.CA); Functional Analysis (math.FA) MSC classes: 42B25, 46E35: Cite as: arXiv:1309.1535 [math.CA] " - On the regularity of maximal operators

On the regularity of maximal operators

On the endpoint regularity of discrete maximal operators

Web9 de jun. de 2003 · On the regularity of maximal operators supported by submanifolds. Journal of Mathematical Analysis and Applications, Vol. 453, Issue. 1, p. 144. CrossRef; … Web1 de dez. de 2024 · The regularity theory of maximal operators is an active topic of current re-search. This program was initiated in the seminal w ork of Kinnunen [10]w h o.

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Web1 de jan. de 2024 · This paper is devoted to studying Sobolev regularity properties of commutators of Hardy–Littlewood maximal operator and its fractional case with Lipschitz symbols, both in the global and local case. Some new pointwise estimates for the weak gradients of the above commutators will be established. As applications, some bounds … Web1 de set. de 2024 · Another way to extend the regularity theory of maximal operators is to study its behavior on different smooth function spaces. Particularly, Korry [12] , [13] …

Web19 de out. de 2024 · Here, we show that the same happens for a class of degenerate second-order operators. We deduce maximal regularity from the R-boundedness of … WebAbstract. We investigate the regularity properties of the two-dimensional one-sided Hardy-Littlewood maximal operator. We point out that the above operator is bounded and continuous on the Sobolev spaces for and .More importantly, we establish the sharp boundedness and continuity for the discrete two-dimensional one-sided Hardy …

Web12 de jan. de 2010 · On the regularity of maximal operators supported by submanifolds. Journal of Mathematical Analysis and Applications, Vol. 453, Issue. 1, p. 144. CrossRef; … WebOn the regularity of maximal operators Emanuel Carneiro Department of Mathematics, University of Texas at Austin, Austin, TX 78712-1082. [email protected] and …

Web1 de jun. de 2024 · It should be pointed out that the fractional maximal operators M α,G and M α,G were first introduced by Liu and Zhang [23] who investigated the Lebesgue …

WebON THE REGULARITY OF MAXIMAL OPERATORS EMANUEL CARNEIRO AND DIEGO MOREIRA Abstract. We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps W 1,p(R) × W,q(R) → W1,r(R) with 1 <∞ and r≥ 1, boundedly and continuously. The same result holds on Rn when r>1. flower shop finaghyWebThis paper will be devoted to study the regularity and continuity properties of the following local multilinear fractional ... will be devoted to study the regularity and continuity properties of the following local multilinear fractional type maximal operators, $$\mathfrak{M}_{\alpha,\Omega}(\vec{f})(x)=\sup\limits_{0<{\rm dist}(x ... flower shop floor planWebThe regularity of maximal operators has also been studied on other spaces and for other maximal operators. We focus on the endpoint p= 1. For example in [12] Carneiro and Svaiter and in [8] and Carneiro and Gonz alez-Riquelme consider convolution maximal operators associated to certain partial di erential equations. flower shop flat shoals rd atlanta gaWeb28 de jul. de 2008 · On the regularity of maximal operators. We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps W … green bay first church green bay wiWeb24 de fev. de 2024 · On the regularity and continuity of the multilinear fractional strong maximal operators. Feng Liu, Corresponding Author. Feng Liu [email protected] ... main purpose of this paper is to study the regularity and continuity properties of the multilinear fractional strong maximal operators associated with rectangles M α, R (f ... green bay first coachWebThis is an expository paper on the regularity theory of maximal operators, when these act on Sobolev and BV functions, with a special focus on some of the current open problems in the topic. Overall, a list of fifteen research problems is presented. It summarizes the contents of a talk delivered by the author at the CIMPA 2024 Research School - … flower shop floral storageWeb23 de dez. de 2016 · The purpose of this work is to show that the fractional maximal operator has somewhat unexpected regularity properties. The main result shows that the fractional maximal operator maps L p-spaces boundedly into certain first-order Sobolev spaces.It is also proved that the fractional maximal operator preserves first-order … flower shop fayetteville nc