Frontiers of Mathematics in China >
Equivalent characterizations of Hardy spaces with variable exponent via wavelets
Received date: 14 Jun 2018
Accepted date: 25 Jun 2019
Published date: 15 Aug 2019
Copyright
Via the boundedness of intrinsic g-functions from the Hardy spaces with variable exponent, , into Lebesgue spaces with variable exponent, , and establishing some estimates on a discrete Littlewood-Paley g-function and a Peetre-type maximal function, we obtain several equivalent characterizations of 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 by elaborately using an observation and the Fefferman-Stein vector-valued maximal inequality on , and also overcome the difficulty of the failure of q = 2 in the atomic decomposition of by a known idea.
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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