# Hokkaido Mathematical Journal

## 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 the Cauchy integral, Calderón-Zygmund operator, Hardy space, local Hardy space.