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The dual of Hardy spaces on a bounded domain in ℝ n

The dual of Hardy spaces on a bounded domain in ℝ n Abstract. We obtain the dual spaces of local Hardy spaces Af () and hpz(Q) for 0 < p < l on a bounded Lipschitz domain . 1991 Mathematics Subject Classification: 42B30 §0. Introduction The basic harmonic analysis on the Euclidean space IR" is well developed. The theories of fractional Integration and of singular integral operators, which are linked closely with the regularity of Solutions of constant coefficient elliptic partial differential operators, form a powerful collection of tools that can be used to attack a variety of problems. New spaces - the real variable Hardy spaces of Stein-Weiss [SW1] and Fefferman-Stein [FS] and the space of functions of bounded mean oscillation (see Fefferman [F] and [FS]) - have been developed, along with their interpolation-theoretic and mapping properties, to round out the "constant coefficient picture". The developments described in the last paragraph are closely tied with the groups that act naturally on Euclidean space: translations, rotations, and dilations. Indeed the profound impact that these groups have on the analysis of Euclidean space is one of the principal themes of the books written by Stein [Sl] and Stein-Weiss [SW2]. Since variable coefficient operators do not respect the action of these groups, http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

The dual of Hardy spaces on a bounded domain in ℝ n

Chang, Der-Chen
Forum Mathematicum , Volume 6 (6) – Jan 1, 1994
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Publisher
de Gruyter
Copyright
Copyright © 2009 Walter de Gruyter
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/form.1994.6.65
Publisher site
See Article on Publisher Site

Abstract

Abstract. We obtain the dual spaces of local Hardy spaces Af () and hpz(Q) for 0 < p < l on a bounded Lipschitz domain . 1991 Mathematics Subject Classification: 42B30 §0. Introduction The basic harmonic analysis on the Euclidean space IR" is well developed. The theories of fractional Integration and of singular integral operators, which are linked closely with the regularity of Solutions of constant coefficient elliptic partial differential operators, form a powerful collection of tools that can be used to attack a variety of problems. New spaces - the real variable Hardy spaces of Stein-Weiss [SW1] and Fefferman-Stein [FS] and the space of functions of bounded mean oscillation (see Fefferman [F] and [FS]) - have been developed, along with their interpolation-theoretic and mapping properties, to round out the "constant coefficient picture". The developments described in the last paragraph are closely tied with the groups that act naturally on Euclidean space: translations, rotations, and dilations. Indeed the profound impact that these groups have on the analysis of Euclidean space is one of the principal themes of the books written by Stein [Sl] and Stein-Weiss [SW2]. Since variable coefficient operators do not respect the action of these groups,

Journal

Forum Mathematicum – de Gruyter

Published: Jan 1, 1994

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