Abstract
In this work we study some properties of the holomorphic TriebeI-Lizorkin spaces HFpqs, 0<p, q≤∞, s∈R, in the unit ball B of Cn, motivated by some well-known properties of the Hardy-Sobolev spaces Hps=HFp2s, 0<p<∞.
We show that ∑n≥0|an|/(n+1)≲||∑n≥0anzn||HF1∞0, which improves the classical Hardy's inequality for holomorphic functions in the Hardy space H1 in the disc. Moreover, we give a characterization of the dual of HF1qs, which includes the classical result (H1)∗=BMOA. Finally, we prove some embeddings between holomorphic Triebel-Lizorkin and Besov spaces, and we apply them to obtain some trace theorems.
Citation
Joaquín M. Ortega. Joan Fàbrega. "Hardy's inequality and embeddings in holomorphic Triebel-Lizorkin spaces." Illinois J. Math. 43 (4) 733 - 751, Winter 1999. https://doi.org/10.1215/ijm/1256060689
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