Riesz Transform Characterizations of Hardy Spaces Associated to Degenerate Elliptic Operators

摘要

Let L-w := -w(-1) div(A del) be the degenerate elliptic operator on the Euclidean space R-n, where w is a Muckenhoupt A(2)(R-n) weight. In this article, the authors establish the Riesz transform characterization of the Hardy space H-Lw(p) (R-n) associated with L-w, for w is an element of A(q)(R-n) boolean AND RH n-2 (R-n) with n >= 3, q is an element of [1, 2] and p is an element of (q(1/r + q-1/2 + 1)(-1), 1] if, for some r is an element of (1, 2], {tL(w)e(-tLw)}(t >= 0) satisfies the weighted L-r - L-2 full off-diagonal estimates.