IMBEDDING AND MULTIPLIER THEOREMS FOR DISCRETE LITTLEWOOD-PALEY SPACES

We prove imbedding and multiplier theorems for discrete Littlewood-Pal ey spaces introduced by M. Frazier and B. Jawerth in their theory of w avelet-type decompositions of Triebel-Lizorkin spaces. The correspondi ng inequalities for discrete spaces defined in terms of characteristic functions of dyadic cubes, with respect to an arbitrary positive loca lly finite measure on the Euclidean space, are useful in the theory of tent spaces, weighted inequalities, duality theorems, interpolation b y analytic and harmonic functions, etc. Our main tools are vector-valu ed maximal inequalities, a dyadic version of the Carleson measure theo rem, and Pisier's factorization lemma. We also consider more general i nequalities, with an arbitrary family of measurable functions in place of characteristic functions of dyadic cubes, which occur in the facto rization theory of operators.