On Higher Riesz Transforms for Gaussian Measures

摘要

Given an n × n matrix B, positive definite and symmetric, let LBbe the differential operator in Rngiven by$L_B=frac{1}{2}Delta -Bxcdot mbox{grad}_x.$A class of higher Riesz transforms associated with LBis defined by means of higher gradients of order k. It is shown that these transformations are bounded in the space$L^p, 1