DOI: 10.1515/gmj-2026-3026 ISSN: 1072-947X

Characterization of parabolic H 1 Sobolev spaces by square functions

Shuichi Sato
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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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