Hardy spaces and BMO-functions induced by ergodic-flows
type: Item
instance of: scholarly article
title: Hardy spaces and BMO-functions induced by ergodic-flows
zbMATH Open document ID: 0614.46044
author: Yanyan Li
published in: Michigan Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: The author studies the Hardy spaces \(H^ p(X)\) associated with ergodic flows which were introduced by \textit{R. R. Coifman} and \textit{G. Weiss} [Proc. Nat. Acad. Sci. USA 70, 1761-1763 (1973; Zbl 0257.46077)]. The main attention lies on the ergodic generalization of BMO functions. In particular, a new proof is given of the fact that the dual of \(H^ 1(X)\) is BMO(X). Some unusual properties of the ergodic Hilbert transform are discussed. The author also extends a theorem of \textit{K. Petersen} [Proc. Am. Math. Soc. 79, 549-555 (1980; Zbl 0442.28020)] on the existence of unbounded (ergodic) VMO functions. The last section of the paper contains another proof of the result that \(H^{\infty}(X)\) is a weak-*-Dirichlet algebra.
reviewed by: Raymond Mortini
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 46J30
Mathematics Subject Classification ID: 47A35
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 44A15
Mathematics Subject Classification ID: 42A50
zbMATH DE Number: 3994302
zbMATH Keywords: Hardy spaces
zbMATH Keywords: ergodic flows
zbMATH Keywords: ergodic generalization of BMO functions
zbMATH Keywords: unbounded (ergodic) VMO functions
zbMATH Keywords: weak-*-Dirichlet algebra
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003242
OpenAlex ID: W2035908679
DOI: 10.1307/MMJ/1029003242
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description: scientific article; zbMATH DE number 3994302