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 $1<p\leq 2$ 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.
Citation
Dashan FAN. Shuichi SATO. "Singular and fractional integrals along variable surfaces." Hokkaido Math. J. 35 (1) 61 - 85, February 2006. https://doi.org/10.14492/hokmj/1285766308
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