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The purpose of this paper is to obtain a discrete version for the Hardy spaces of the weak factorization results obtained for the real Hardy spaces 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...
We study various characterizations of the Hardy spaces via the discrete Hilbert transform and via maximal and square functions. Finally, we present the equivalence with the classical atomic characterization of given by Coifman and Weiss in [CW]. Our proofs are based on some results concerning functions of exponential type.
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