On the regularity of maximal operators
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 … WebThe regularity of a maximal operator was rst studied in [Kin97], where Kinnunen proved that for p>1 and f2W1;p(Rd) the bound krMfk p C d;pkrfk p (1.1) holds, from which it follows that the Hardy-Littlewood maximal operator is bounded on W1;p(Rd). Originally, Kinnunen proved (1.1) only for the Hardy-Littlewood maximal operator which averages
On the regularity of maximal operators
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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 … 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.
WebPROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 144, Number 5, May 2016, Pages 2015–2028 http://dx.doi.org/10.1090/proc/13012 Article … 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 …
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 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 …
WebThis 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 - …
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 … ina bromma andreas hambergerincense harvestingWeb22 de dez. de 2009 · We prove weighted estimates for the maximal regularity operator. Such estimates were motivated by boundary value problems. We take this opportunity to study a class of weak solutions to the abstract Cauchy problem. We also give a new proof of maximal regularity for closed and maximal accretive operators following from Kato’s … ina budde physiotheraeutiWebThis 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 ... ina brown fresno ca sistersWeb12 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; … ina brotherWebRemark 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. incense hanging burnerWeb23 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 … incense for selling food