An Integrability Theorem on Unbounded Vilenkin Groups

An analogue of the classical Fomin′s theorem holds in general Vilenkin systems. We prove this using F. Riesz′s general version of the Hausdorff-Young inequality on the cosets of a subgroup of a given Vilenkin group. The class of sequences involved and the class of quasiconvex sequences are incompara...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 175; no. 2; pp. 438 - 447
Main Authors Avdispahic, M., Pepic, M.
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 15.05.1993
Elsevier
Subjects
Abstract harmonic analysis
Exact sciences and technology
Mathematical analysis
Mathematics
Sciences and techniques of general use
Partial sum
Sequence
Abelian group
Integrability
Compact group
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Summary:An analogue of the classical Fomin′s theorem holds in general Vilenkin systems. We prove this using F. Riesz′s general version of the Hausdorff-Young inequality on the cosets of a subgroup of a given Vilenkin group. The class of sequences involved and the class of quasiconvex sequences are incomparable.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1993.1182