Pointwise estimates to the modified Riesz potential

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Harjulehto , P & Hurri-Syrjänen , R 2018 , ' Pointwise estimates to the modified Riesz potential ' , Manuscripta Mathematica , vol. 156 , no. 3-4 , pp. 521-543 . https://doi.org/10.1007/s00229-017-0983-y

Title: Pointwise estimates to the modified Riesz potential
Author: Harjulehto, Petteri; Hurri-Syrjänen, Ritva
Contributor organization: Department of Mathematics and Statistics
Geometric Analysis and Partial Differential Equations
Date: 2018-07
Language: eng
Number of pages: 23
Belongs to series: Manuscripta Mathematica
ISSN: 0025-2611
DOI: https://doi.org/10.1007/s00229-017-0983-y
URI: http://hdl.handle.net/10138/307540
Abstract: In a smooth domain a function can be estimated pointwise by the classical Riesz potential of its gradient. Combining this estimate with the boundedness of the classical Riesz potential yields the optimal Sobolev-Poincar, inequality. We show that this method gives a Sobolev-Poincar, inequality also for irregular domains whenever we use the modified Riesz potential which arise naturally from the geometry of the domain. The exponent of the Sobolev-Poincar, inequality depends on the domain. The Sobolev-Poincar, inequality given by this approach is not sharp for irregular domains, although the embedding for the modified Riesz potential is optimal. In order to obtain the results we prove a new pointwise estimate for the Hardy-Littlewood maximal operator.
Subject: 111 Mathematics
Peer reviewed: Yes
Rights: unspecified
Usage restriction: openAccess
Self-archived version: acceptedVersion

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