QUANTITATIVE WEIGHTED L-p BOUNDS FOR THE MARCINKIEWICZ INTEGRAL

摘要

Let Omega be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and mu(Omega) be the higher-dimensional Marcinkiewicz integral associated with Omega. In this paper, the authors proved that if Omega is an element of L-q(Sn-1) for some q is an element of (1, infinity], then for p is an element of (q', infinity) and w is an element of A(p)(R-n), the bound of mu Omega on L-p(R-n, w) is less than C[w](Ap/q')(max{1/2, 1/p-q'}+max{1, q'/p-q'}).