×

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.)
PDF BibTeX XML Cite
Full Text: DOI