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.