The Variation of the Fractional Maximal Function of a Radial Function

被引：31

作者：

Luiro, Hannes ^{[1
]}

Madrid, Jose ^{[2
,3
]}

机构：

[1] Univ Jyvaskyla, Dept Math & Stat, POB 35 MaD, Jyvaskyla 40014, Finland

[2] Aalto Univ, Dept Math, POB 11100, FI-00076 Aalto, Finland

[3] Abdus Salam Int Ctr Theoret Phys, Str Costiera 11, I-34151 Trieste, Italy

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2019年 / 2019卷 / 17期

基金：

芬兰科学院;

关键词：

REGULARITY;

D O I：

10.1093/imrn/rnx277

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we study the regularity of the non-centered fractional maximal operator M-beta. As the main result, we prove that there exists C(n, beta) such that if q = n/(n - beta) and f is radial function, then parallel to DM(beta)f parallel to(Lq(Rn)) <= C(n, beta) parallel to Df parallel to(L1(Rn)). The corresponding result was previously known only if n = 1 or beta = 0. Our proofs are almost free from one-dimensional arguments. Therefore, we believe that the new approach may be very useful when trying to extend the result for all f is an element of W-1,W-1(R-n).

引用

页码：5284 / 5298

页数：15

共 19 条

[1] Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities [J].

Aldaz, J. M. ;

Perez Lazaro, J. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 359 (05) :2443-2461

[2]

[Anonymous], 2013, J FUNCT ANAL, DOI DOI 10.1016/J.JFA.2013.05.012

[3] ON A DISCRETE VERSION OF TANAKA'S THEOREM FOR MAXIMAL FUNCTIONS [J].

Bober, Jonathan ;

Carneiro, Emanuel ;

Hughes, Kevin ;

Pierce, Lillian B. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2012, 140 (05) :1669-1680

[4] On the regularity of maximal operators [J].

Carneiro, Emanuel ;

Moreira, Diego .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (12) :4395-4404

[5] Endpoint Sobolev and BV continuity for maximal operators [J].

Carneiro, Emanuel } ;

Madrid, Jose ;

Pierce, Lillian B. .

JOURNAL OF FUNCTIONAL ANALYSIS, 2017, 273 (10) :3262-3294

[6] DERIVATIVE BOUNDS FOR FRACTIONAL MAXIMAL FUNCTIONS [J].

Carneiro, Emanuel ;

Madrid, Jose .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2017, 369 (06) :4063-4092

[7]

Carneiro E, 2012, MATH RES LETT, V19, P1245

[8]

Hajlasz P, 2004, ANN ACAD SCI FENN-M, V29, P167

[9]

Hajlasz P, 2010, P AM MATH SOC, V138, P165

[10] Regularity of the fractional maximal function [J].

Kinnunen, J ;

Saksman, E .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2003, 35 :529-535

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