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Factorization of sequences in discrete Hardy spaces

Santiago Boza — 2012

Studia Mathematica

The purpose of this paper is to obtain a discrete version for the Hardy spaces H p ( ) of the weak factorization results obtained for the real Hardy spaces H p ( ) 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...

Discrete Hardy spaces

Santiago BozaMaría Carro — 1998

Studia Mathematica

We study various characterizations of the Hardy spaces H p ( ) via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of H p ( ) given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.

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