Banach Journal of Mathematical Analysis

Wavelet characterizations of Musielak–Orlicz Hardy spaces

Xing Fu and Dachun Yang

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Abstract

In this article, via establishing a new atomic characterization of the Musielak–Orlicz Hardy space Hφ(Rn) [which is essentially deduced from the known molecular characterization of Hφ(Rn)] and some estimates on a new discrete Littlewood–Paley g-function and a Peetre-type maximal function, together with using the known intrinsic g-function characterization of Hφ(Rn), the authors obtain several equivalent characterizations of Hφ(Rn) in terms of wavelets, which extend the wavelet characterizations of both Orlicz–Hardy spaces and the weighted Hardy spaces, and are available to the typical and useful Musielak–Orlicz Hardy space Hlog(Rn). The novelty of this approach is that the new adapted atomic characterization of Hφ(Rn) compensates the inconvenience in applications of the supremum appearing in the original definition of atoms, which play crucial roles in the proof of the main theorem of this article and may have further potential applications.

Article information

Source
Banach J. Math. Anal., Volume 12, Number 4 (2018), 1017-1046.

Dates
Received: 29 November 2017
Accepted: 26 March 2018
First available in Project Euclid: 4 September 2018

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1536048016

Digital Object Identifier
doi:10.1215/17358787-2018-0010

Mathematical Reviews number (MathSciNet)
MR3858759

Zentralblatt MATH identifier
06946301

Subjects
Primary: 42C40: Wavelets and other special systems
Secondary: 42B30: $H^p$-spaces 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B25: Maximal functions, Littlewood-Paley theory

Keywords
Musielak–Orlicz Hardy space wavelet atom Peetre-type maximal function Littlewood–Paley g-function

Citation

Fu, Xing; Yang, Dachun. Wavelet characterizations of Musielak–Orlicz Hardy spaces. Banach J. Math. Anal. 12 (2018), no. 4, 1017--1046. doi:10.1215/17358787-2018-0010. https://projecteuclid.org/euclid.bjma/1536048016


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