# Hokkaido Mathematical Journal

## Hokkaido Mathematical Journal, 35 (2006) pp.61-85

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### Abstract

We study singular integrals associated with the variable surfaces of revolution. We treat the rough kernel case where the singular integral is defined by an $H^1$ kernel function on the sphere $S^{n-1}$. We prove the $L^p$ boundedness of the singular integral for $11$. We also study the $(L^p,L^r)$ boundedness for fractional integrals associated with surfaces of revolution.

MSC(Primary) 42B20 Singular integral, Hardy space, Rough kernel, Fractional integral