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Endpoint Regularity of Multisublinear Fractional Maximal Functions

  Published:2016-08-30
 Printed: Sep 2017
  • 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

In this paper we investigate the endpoint regularity properties of the multisublinear fractional maximal operators, which include the multisublinear Hardy-Littlewood maximal operator. We obtain some new bounds for the derivative of the one-dimensional multisublinear fractional maximal operators acting on vector-valued function $\vec{f}=(f_1,\dots,f_m)$ with all $f_j$ being $BV$-functions.
Keywords: multisublinear fractional maximal operators, Sobolev spaces, bounded variation multisublinear fractional maximal operators, Sobolev spaces, bounded variation
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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