Hardy's inequality and embeddings in holomorphic Triebel-Lizorkin spaces

In this work we study some properties of the holomorphic Triebel-Lizorkin s paces H F-s(pq), 0 < p, q less than or equal to infinity, s is an element o f R, in the unit ball B of C-n, motivated by some well-known properties of the Hardy-Sobolev spaces H-s(p) = HFsp2, 0 < p < infinity. We show that Sigma(n greater than or equal to 0) \a(n)\/(n + 1) less than o r similar to \\ Sigma(n greater than or equal to 0) a(n)z(n)\\(H F0loc), wh ich improves the classical Hardy's inequality for holomorphic functions in the Hardy space H-1 in the disc. Moreover, we give a characterization of th e dual of H F-s(1q), which includes the classical result (H-1)* = BMOA. Fin ally, we prove some embeddings between holomorphic Triebel-Lizorkin and Bes ov spaces, and we apply them to obtain some trace theorems.