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This is a Quantitative Study study.

September 12, 2025Studia Mathematica

Discrete Hardy spaces

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This work establishes connections between hardy spaces and the discrete Hilbert transform, facilitating new insights.
The research demonstrates that the atomic characterization aligns with foundational results from Coifman and Weiss.
Methods involve exploring functions of exponential type to underline the underlying structure of these spaces.
The findings call for a reevaluation of existing frameworks relating to discrete functional analysis.

Implication

This analysis reveals equivalence of hardy spaces with maximal functions in discrete cases, indicating deeper connections.

Abstract

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

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Cite This Study

Santiago Boza (1998) studied this question.

synapsesocial.com/papers/68d4768331b076d99fa6f206 https://doi.org/10.4064/sm-129-1-31-50

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Implication

This analysis reveals equivalence of hardy spaces with maximal functions in discrete cases, indicating deeper connections.

Discrete Hardy spaces

Key Points

Implication

Abstract

Discussion

Cite This Study

Discrete Hardy spaces

Key Points

Implication

Abstract

Discussion

Cite This Study

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