We show that for any q > 0, b real, and tempered distribution f, the statement that m(x,t) = (t^b || p_t * f (x)|)^q t^-1 dxdt is a Carleson measure does not depend on the kernel p (satisfying the standard Tauberian condition and a moment condition of order [-b]); and this characterizes a "Triebel-Lizorkin" space for q=infinity. Since the above characterizes BMO when q=2 and b=0 (by results of Fefferman-Stein and others), we obtain a new proof in this well-known case. (Joint with M.H. Taibleson.)