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Some characterizations of Hardy spaces associated with twisted convolution. (English) Zbl 1180.42012

The Hardy space \(H^{1}(\mathbb{C}^{n})\) associated with twisted convolution is initially defined by G. Mauceri, M. Picadello and F. Ricci [Adv. Math. 39, 270–288 (1981; Zbl 0503.46037)]. They gave some characterization of it via maximal function, atomic decomposition and Riesz transform. In this paper the author obtains other characterizations of the Hardy space \(H^{1}(\mathbb{C}^{n})\) associated with twisted convolution in terms of Lusin area integral, Littlewood-Paley \(g\)-function by using heat maximal function and the atomic decomposition in the tent space.

MSC:

42B30 \(H^p\)-spaces
42B25 Maximal functions, Littlewood-Paley theory
42B35 Function spaces arising in harmonic analysis

Citations:

Zbl 0503.46037
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References:

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