A Look at BMO_ϕ(ω) through Carleson Measures

Abstract

As Fefferman and Stein showed, there is a tight connection between Carleson measures and BMO functions. In this work we extend this type of results to the more general scope of the BMO_ϕ(ω) spaces. As a byproduct a weighted version of the Triebel-Lizorkin space $\dot{F}^0_{\infty, 2}$ is introduced, which turns out to be isomorphic to BMO(ω) as in the unweighted case.