Factorization of tent spaces and Hankel operators

It is shown that the factorization T-q(p) = T-proportional to(p), T-q(infin ity) for tent spaces proved by R. R. Coifman et al. (1985, J. Funct. Anal. 62, 304-335) for p > q, q = 2, holds true for all 0 < p, q < infinity. From this certain strong factorization theorems are derived for spaces H-s(p) o f fractional derivatives of H-p functions, and more general Triebel spaces. In particular, it is proved that H-s(p) = H-p. BMOA(s). Applications consi dered include characterizations of symbols of bounded Hankel operators H-ph i-:H-p --> H-s(q), complex interpolation of tent spaces, and Carleson measu re theorems for derivatives of H-p functions. (C) 2000 Academic Press.