Equivalency between the Generalized Carleson Measure Spaces and Triebel-Lizorkin-Type Spaces

In this note, we show that the homogeneous Triebel-Lizorkin-type spaces $\dot{F}^{\alpha,\tau}_{p,q}$ with four parameters defined in \cite{yy1,yy2} is essentially same as the generalized Carleson measure space $CMO^{\alpha,q}_r$ introduced in \cite{lw} with equivalent norms.