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Generalized Lipschitz Spaces on Vilenkin Groups
Author(s) -
Bloom Walter R.,
Fournier John J. F.
Publication year - 1987
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19871320106
Subject(s) - mathematics , lipschitz continuity , fourier series , pure mathematics , extension (predicate logic) , series (stratigraphy) , hardy space , convergence (economics) , mathematical analysis , paleontology , computer science , economics , biology , programming language , economic growth
It is shown that, for certain choices of the defining indices, the generalized Lipschitz spaces on Vilenkin groups are included in certain Figà‐Talamanca spaces A p , and that the Fourier series of functions in the latter spaces converge uniformly. This result includes an extension of the classical Dini test, and endpoint versions of Bernstein's theorem on absolute convergence of Fourier series.