Characterizes H1 Sobolev spaces using square functions, suggesting new insights into their properties.
We consider <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>H</m:mi> <m:mn>1</m:mn> </m:msup> </m:math> {H¹} -Sobolev spaces associated with the Calderón–Torchinsky Hardy spaces <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>H</m:mi> <m:mn>1</m:mn> </m:msup> </m:math> {H¹} 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 (2026) studied this question.
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