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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


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1435-5337
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Volume 27, Issue 5

Issues

Fractional type Marcinkiewicz integral operators on function spaces

Qingying Xue
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, P. R. China
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/ Kôzô Yabuta
  • Research Center for Mathematical Sciences, Kwansei Gakuin University, Gakuen 2-1, Sanda 669-1337, Japan
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  • De Gruyter OnlineGoogle Scholar
/ Jingquan Yan
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing, 100875, P. R. China
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Published Online: 2014-02-19 | DOI: https://doi.org/10.1515/forum-2013-0200

Abstract

In this paper, we discussed about the boundedness of the fractional type Marcinkiewicz integral operators, and improved a result given by Chen, Fan and Ying in 2002. They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel–Lizorkin spaces F˙pqα(n) to Lp(n). We greatly weakened their assumptions and extended their results to a pretty much more general way.

Keywords: Lp boundedness; Marcinkiewicz integral; fractional integral operator; Triebel–Lizorkin spaces; Sobolev spaces

MSC: 42B20; 42B25; 47G10

About the article

Received: 2013-12-12

Revised: 2013-12-23

Published Online: 2014-02-19

Published in Print: 2015-09-01


Funding Source: NSF of China

Award identifier / Grant number: 10931001

Funding Source: Grant-in-Aid for Scientific Research (C), Japan Society for the Promotion of Science

Award identifier / Grant number: 23540228

Funding Source: Program for Changjiang Scholars and Innovative Research Team in University

Funding Source: NCET-13-0065


Citation Information: Forum Mathematicum, Volume 27, Issue 5, Pages 3079–3109, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2013-0200.

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[2]
Yoshihiro Sawano and Kôzô Yabuta
Journal of Inequalities and Applications, 2014, Volume 2014, Number 1, Page 232

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