L^p BOUNDS FOR NONISOTROPIC MARCINKIEWICZ INTEGRALS ASSOCIATED TO SURFACES. (17th August 2015) - LIU, FENG; MAO, SUZHEN
Abstract : In an extrapolation argument, we prove certain L^p (1<p<∞ ) estimates for nonisotropic Marcinkiewicz operators associated to surfaces under the integral kernels given by the elliptic sphere functions ΩL(^+L)^α(Σ) and the radial function hN_β(R^+) . As applications, the corresponding results for parametric Marcinkiewicz integral operators related to area integrals and Littlewood–Paley g_λ^* -functions are given.