Imbedding and multiplier theorems for discrete Littlewood-Paley spaces
Imbedding and multiplier theorems are proved for discrete Littlewood-Paley spaces introduced by M. Frazier and B. Jawerth in their theory of wavelet-type decompositions of Triebel-Lizorkin spaces. The corresponding inequalities for discrete spaces (defined in terms of characteristic functions of dyadic cubes, with respect to an arbitrary locally finite measure on the Euclidean space), are useful in the theory of tent spaces, weighted inequalities, duality theorems, interpolation by analytic and harmonic functions, etc. The proofs make use of vector-valued maximal inequalities, dyadic versions of the Carleson measure theorem, and Pisier's factorization lemma. Some more general inequalities are considered with an arbitrary family of measurable functions in place of characteristic functions of dyadic cubes, which occur in the factorization theory of operators.
scientific article; zbMATH DE number 950232