Atomic decomposition of real-variable type for Bergman spaces in the unit ball of Cn
Chen, Zeqian (Chinese Academy of Sciences. Wuhan Institute of Physics and Mathematics)
Ouyang, Wei (Chinese Academy of Sciences. Institute of Geodesy and Geophysics (Wuhan, Xina))

Date:	2014
Abstract:	In this paper we show that, for any 0 < p _ 1 and _ > 1, every (weighted) Bergman space Ap _(Bn) admits an atomic decomposition of real-variable type. More precisely, for each f 2 Ap _(Bn) there exist a sequence of (p;1)_-atoms ak with compact support and a scalar sequence f_kg such that f = P k _kak in the sense of distribution and Pk j_kjp . kfkp p and moreover, f = Pk _kP_(ak) in Ap_(Bn); where P_ is the orthogonal projection from L2_(Bn) onto A2_(Bn): The proof is constructive and our construction is based on analysis inside the unit ball Bn associated with a quasimetric.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Bergman space ; Atomic decomposition ; Bergman kernel ; Homogeneous space ; Maximal function
Published in:	Publicacions matemàtiques, Vol. 58, Núm. 2 (2014) , p. 353-377, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287181
DOI: 10.5565/PUBLMAT_58214_18

25 p, 436.1 KB

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