Banach Journal of Mathematical Analysis

Intrinsic atomic and molecular decompositions of Hardy–Musielak–Orlicz spaces

Kwok-Pun Ho

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Abstract

We introduce the Hardy type space for Musielak–Orlicz spaces. It includes several existing Hardy type spaces such as the Hardy–Orlicz spaces and the Hardy spaces with variable exponents. Furthermore, we develop an atomic decomposition such that the size condition just relies on the norms of Musielak–Orlicz spaces. This gives us a nature extension of the molecular decompositions to the Hardy type space for Musielak–Orlicz spaces.

Article information

Source
Banach J. Math. Anal., Volume 10, Number 3 (2016), 566-592.

Dates
Received: 24 August 2015
Accepted: 11 November 2015
First available in Project Euclid: 22 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1469199410

Digital Object Identifier
doi:10.1215/17358787-3607354

Mathematical Reviews number (MathSciNet)
MR3528348

Zentralblatt MATH identifier
1346.42024

Subjects
Primary: 42B30: $H^p$-spaces
Secondary: 42B25: Maximal functions, Littlewood-Paley theory 42B35: Function spaces arising in harmonic analysis 46E30: Spaces of measurable functions (Lp-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)

Keywords
atomic decomposition molecular decomposition Hardy spaces Musielak–Orlicz spaces

Citation

Ho, Kwok-Pun. Intrinsic atomic and molecular decompositions of Hardy–Musielak–Orlicz spaces. Banach J. Math. Anal. 10 (2016), no. 3, 566--592. doi:10.1215/17358787-3607354. https://projecteuclid.org/euclid.bjma/1469199410


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