On singular integrals and maximal operators along surfaces of revolution on product domains

Abstract

. We study the mapping properties of singular integral operators along surfaces of revo-lutions on product domains. For several classes of surfaces, we prove sharp L p bounds ( 1 < p <  ) for these singular integral operators as well as their corresponding maximal operators. By using these L p bounds and an extrapolation argument we obtain the L p boundedness of these operators under optimal conditions on the singular kernels. Our results extend and improve several results previously obtained by many authors.