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Generalized Lipschitz Spaces on Vilenkin Groups

✍ Scribed by Walter R. Bloom; John J. F. Fournier

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
550 KB
Volume
132
Category
Article
ISSN
0025-584X

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✦ Synopsis

It is shown that, for certain choices of the defining indices, the generalized LIPSCHITZ spaces on VILEWKIJ groups are incIudec1 in certain FIGA-TALAXAYCA spaces A,, and t h a t the FOURIER series of functions in the letter spaces converge uniformly. This result includes an extension of the classical DIN test, and endpoint versions of BERNSTEIN'S theorem on absolute convergence of FOURIER series.

m =n ..exists x,€G,,\G,+~ such that Q),(x,,) =exp ( 2 7 ~i p ; ; ~) , and each xEG has a unique representationb,x, where 0 s b, <pn + l . n =O *) Research partially supported by NSERC Grant # 4822.

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