Generalized Carleson Measure Spaces and Their Applications

Abstract

We introduce the generalized Carleson measure spaces CMOrα,q that extend BMO. Using Frazier and Jawerth's φ-transform and sequence spaces, we show that, for α∈R and 0<p≤1, the duals of homogeneous Triebel-Lizorkin spaces Ḟpα,q for 1<q<∞ and 0<q≤1 are CMO(q'/p)-(q'/q)-α,q' and CMOr-α+(n/p)-n,∞ (for any r∈R), respectively. As applications, we give the necessary and sufficient conditions for the boundedness of wavelet multipliers and paraproduct operators acting on homogeneous Triebel-Lizorkin spaces.