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Maximal function characterizations of Hardy spaces associated to homogeneous higher order elliptic operators

Jun Cao, Svitlana Mayboroda and Dachun Yang
From the journal Forum Mathematicum

Abstract

Let L be a homogeneous divergence form higher order elliptic operator with complex bounded measurable coefficients and (p-(L),p+(L)) be the maximal interval of exponents q[1,] such that the semigroup {e-tL}t>0 is bounded on Lq(n). In this article, the authors establish the non-tangential maximal function characterizations of the associated Hardy spaces HLp(n) for all p(0,p+(L)), which when p=1, answers a question asked by Deng, Ding and Yao in [21]. Moreover, the authors characterize HLp(n) via various versions of square functions and Lusin-area functions associated to the operator L.


Communicated by Christopher D. Sogge


Funding source: National Science Foundation

Award Identifier / Grant number: DMS 1220089

Award Identifier / Grant number: DMS 1344235

Award Identifier / Grant number: DMR 0212302

Funding source: National Natural Science Foundation of China

Award Identifier / Grant number: 11501506

Award Identifier / Grant number: 11571039

Award Identifier / Grant number: 11361020

Funding statement: J. Cao is supported by the National Natural Science Foundation of China (grant no. 11501506) and the Natural Science Foundation of Zhejiang University of Technology (grant no. 2014XZ011). S. Mayboroda was partially supported by the NSF grants DMS 1220089 (CAREER), DMS 1344235 (INSPIRE), DMR 0212302 (UMN MRSEC Seed grant) and the Alfred P. Sloan Fellowship. D. Yang is supported by the National Natural Science Foundation of China (grant no. 11571039 and 11361020), the Specialized Research Fund for the Doctoral Program of Higher Education of China (grant no. 20120003110003) and the Fundamental Research Funds for the Central Universities of China (grant no. 2013YB60 and 2014KJJCA10).

The authors would like to thank the referee for his very carefully reading and many stimulating remarks which do improve the presentation of this article.

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Received: 2014-7-15
Revised: 2015-4-21
Published Online: 2015-10-1
Published in Print: 2016-9-1

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