Fractional type Marcinkiewicz integral operators on function spaces

Qingying Xue; Kôzô Yabuta; Jingquan Yan

doi:10.1515/forum-2013-0200

Published by De Gruyter February 19, 2014

Fractional type Marcinkiewicz integral operators on function spaces

Qingying Xue , Kôzô Yabuta and Jingquan Yan

From the journal Forum Mathematicum

https://doi.org/10.1515/forum-2013-0200

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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(ℝn) to Lp(ℝn). 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

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

The authors want to express their sincerely thanks to the referee for his or her valuable remarks and suggestions which made this paper more readable.

Received: 2013-12-12

Revised: 2013-12-23

Published Online: 2014-2-19

Published in Print: 2015-9-1

Fractional type Marcinkiewicz integral operators on function spaces

Abstract

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