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On the Regularity of the Multisublinear Maximal Functions

  Published:2015-02-24
 Printed: Dec 2015
  • Feng Liu,
    College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, Shandong 266590, P. R. China
  • Huoxiong Wu,
    School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, P. R. China
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Abstract

This paper is concerned with the study of the regularity for the multisublinear maximal operator. It is proved that the multisublinear maximal operator is bounded on first-order Sobolev spaces. Moreover, two key point-wise inequalities for the partial derivatives of the multisublinear maximal functions are established. As an application, the quasi-continuity on the multisublinear maximal function is also obtained.
Keywords: regularity, multisublinear maximal operator, Sobolev spaces, partial deviative, quasicontinuity regularity, multisublinear maximal operator, Sobolev spaces, partial deviative, quasicontinuity
MSC Classifications: 42B25, 46E35 show english descriptions Maximal functions, Littlewood-Paley theory
Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
42B25 - Maximal functions, Littlewood-Paley theory
46E35 - Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems
 

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