## Singular and fractional integrals along variable surfaces.(English)Zbl 1129.42354

Summary: We study singular integrals associated with 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 $$1 < p < 2$$ assuming that a certain lower dimensional maximal operator is bounded on $$L^s$$ for all $$s > 1$$. We also study the $$(L^p, L^r)$$ boundedness for fractional integrals associated with surfaces of revolution.

### MSC:

 42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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