Banach Journal of Mathematical Analysis

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

Kwok-Pun Ho

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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

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

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

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Zentralblatt MATH identifier

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.)

atomic decomposition molecular decomposition Hardy spaces Musielak–Orlicz spaces


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.

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