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The aim is to characterize parabolic H1 Sobolev spaces linked to Calderón-Torchinsky Hardy spaces using square functions.

June 27, 2026Georgian Mathematical Journal0 citations

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Characterization of parabolic H 1 Sobolev spaces by square functions

SSShuichi Sato

Key Points

The aim is to characterize parabolic H1 Sobolev spaces linked to Calderón-Torchinsky Hardy spaces using square functions.
Examined the properties of parabolic H1 Sobolev spaces.
Utilized square functions for this characterization.
Compared results with existing knowledge in the Euclidean context.
Characterization provides a new understanding of H1 Sobolev spaces.
Findings improve upon earlier results in the field.
Highlights the relevance of square functions in this mathematical context.

Abstract

Abstract We consider H 1 H^{1} -Sobolev spaces associated with the Calderón–Torchinsky Hardy spaces H 1 H^{1} and characterize these spaces by means of certain square functions. This characterization generalizes and, in fact, improves upon previously known results in the Euclidean setting.

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Shuichi Sato (Thu,) studied this question.

synapsesocial.com/papers/6a3f67e2aea7db3c1953f2b0 https://doi.org/https://doi.org/10.1515/gmj-2026-3026

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Characterization of parabolic H 1 Sobolev spaces by square functions

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