Factorization of Tent Spaces and Hankel Operators

It is shown that the factorization Tpq=Tp∞·T∞q 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<∞. From this certain strong factorization theorems are derived for spaces Hps of fractional derivatives of Hp functions, and more general Triebel spaces. In particular, it is proved that Hps=Hp·BMOAs . Applications considered include characterizations of symbols of bounded Hankel operators Hφ: Hp→Hqs, complex interpolation of tent spaces, and Carleson measure theorems for derivatives of Hp functions.