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Factorization of sequences in discrete Hardy spaces

100%

Boza S.

Studia Mathematica

2012

tom 209

nr 1

53-69

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.

Discrete Hardy spaces

63%

Boza S., Carro M. J.

Studia Mathematica

1998

tom 129

nr 1

31-50

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

Ograniczanie wyników

2 Studia Mathematica

2 Boza S.

1 Carro M. J.

1 2012

1 1998

Wyniki wyszukiwania

Factorization of sequences in discrete Hardy spaces

Discrete Hardy spaces