An Integrability Theorem on Unbounded Vilenkin Groups

• Published in: Journal of mathematical analysis and applications Vol. 175; no. 2; pp. 438 - 447
• Main Authors: Avdispahic, M., Pepic, M.
• Format: Journal Article
• Language: English
• 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

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...