RESEARCH ARTICLE

Equivalent characterizations of Hardy spaces with variable exponent via wavelets

  • Xing FU
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  • Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China

Received date: 14 Jun 2018

Accepted date: 25 Jun 2019

Published date: 15 Aug 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

Via the boundedness of intrinsic g-functions from the Hardy spaces with variable exponent, Hp()(n), into Lebesgue spaces with variable exponent, Lp()(n), and establishing some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function, we obtain several equivalent characterizations of Hp()(n) in terms of wavelets, which extend the wavelet characterizations of the classical Hardy spaces. The main ingredients are that, we overcome the difficulties of the quasi-norms of Hp()(n) by elaborately using an observation and the Fefferman-Stein vector-valued maximal inequality on Lp()(n), and also overcome the difficulty of the failure of q = 2 in the atomic decomposition of Hp()(n) by a known idea.

Cite this article

Xing FU . Equivalent characterizations of Hardy spaces with variable exponent via wavelets[J]. Frontiers of Mathematics in China, 2019 , 14(4) : 737 -759 . DOI: 10.1007/s11464-019-0777-5

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