Hokkaido Mathematical Journal

KOMORI Yasuo,

The Cauchy integral operator on Hardy space.

Hokkaido Mathematical Journal, 37 (2008) pp.389-398

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Abstract

We show that the Cauchy integral operator is bounded from $H^p(R^1)$ to $h^p(R^1)$ (local Hardy space). To prove our theorem we shall introduce generalized atom and consider a variant of "$Tb$ theorem".

MSC(Primary)42B20
MSC(Secondary)
Uncontrolled Keywordsthe Cauchy integral, Calderón-Zygmund operator, Hardy space, local Hardy space.