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Winter 1999 Hardy's inequality and embeddings in holomorphic Triebel-Lizorkin spaces
Joaquín M. Ortega, Joan Fàbrega
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Illinois J. Math. 43(4): 733-751 (Winter 1999). DOI: 10.1215/ijm/1256060689

Abstract

In this work we study some properties of the holomorphic TriebeI-Lizorkin spaces HFpqs, 0<p, q, sR, 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 n0|an|/(n+1)||n0anzn||HF10, 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.

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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

Information

Published: Winter 1999
First available in Project Euclid: 20 October 2009

zbMATH: 0936.32004
MathSciNet: MR1712520
Digital Object Identifier: 10.1215/ijm/1256060689

Subjects:
Primary: 32A37
Secondary: ‎46E15

Rights: Copyright © 1999 University of Illinois at Urbana-Champaign

Vol.43 • No. 4 • Winter 1999
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