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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Brüdern, Jörg / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Neeb, Karl-Hermann / Noguchi, Junjiro / Shahidi, Freydoon / Sogge, Christopher D. / Wienhard, Anna

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Volume 24, Issue 3

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Maximal function characterizations of Hardy spaces associated with magnetic Schrödinger operators

Renjin Jiang
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
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/ Dachun Yang
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
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/ Dongyong Yang
  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, People's Republic of China
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Published Online: 2012-05-01 | DOI: https://doi.org/10.1515/form.2011.067

Abstract.

Let be a magnetic Schrödinger operator on , , where and . In this paper, the authors establish the equivalent characterizations of the Hardy space for , defined by the Lusin area function associated with , in terms of the radial maximal functions and the non-tangential maximal functions associated with and , respectively. This gives an affirmative answer to an open problem of Xuan Thinh Duong et al. [Ark. Mat. 44 (2006), 261–275]. The boundedness of the Riesz transforms , , from to is also presented, where is the closure of in and .

Keywords: Hardy space; magnetic Schrödinger operator; maximal function; Riesz transform

About the article

Received: 2009-04-19

Published Online: 2012-05-01

Published in Print: 2012-05-01


Citation Information: Forum Mathematicum, Volume 24, Issue 3, Pages 471–494, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/form.2011.067.

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