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The purpose of this paper is to obtain a discrete version for the Hardy spaces $H^{p}(ℤ)$ of the weak factorization results obtained for the real Hardy spaces $H^{p}(ℝⁿ)$ by Coifman, Rochberg and Weiss for p > n/(n+1), and by Miyachi for p ≤ n/(n+1). It represents an extension, in the one-dimensional case, of the corresponding result by A. Uchiyama who obtained a factorization theorem in the general context of spaces X of homogeneous type, but with some restrictions on the measure that exclude the case of points of positive measure on X and, hence, ℤ. In order to obtain the factorization theorem, we first study the boundedness of some bilinear maps defined on discrete Hardy spaces.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
53-69
Opis fizyczny
Daty
wydano
2012
Twórcy
autor
- Department of Applied Mathematics IV, EPSEVG, Polytechnical University of Catalonia, E-08880 Vilanova i Geltrú, Spain
Bibliografia
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Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm209-1-5