Journal article
Absolute convergence of Fourier series on totally disconnected groups
Arkiv för matematik, Vol.20(1-2), pp.101-109
1982
Abstract
Let G denote a totally disconnected locally compact metric abelian group with translation invariant metric d and character group ΓG. The Lipschitz spaces are defined by {Mathematical expression} where τaf:x→f(x-a) and α∈(0,1). For a suitable choice of metric it is shown that Lip (α;p)⊂Lr(ΓG), where α>1/p+1/r-1≧0 and 1≦p≦2. In the case G is compact the corresponding result holds for α>1/r-1/2 and p>2. In addition for G non-discrete the above result is shown to be sharp, in the sense that the range of values of α cannot be extended. The results include classical theorems of S. N. Bernstein, O. Szász and E. C. Titchmarsh.
Details
- Title
- Absolute convergence of Fourier series on totally disconnected groups
- Authors/Creators
- W.R. Bloom (Author/Creator) - Murdoch University
- Publication Details
- Arkiv för matematik, Vol.20(1-2), pp.101-109
- Publisher
- Kluwer Academic Publishers
- Identifiers
- 991005541108507891
- Copyright
- © 1982 Institut Mittag Leffler.
- Murdoch Affiliation
- School of Mathematical and Physical Sciences
- Language
- English
- Resource Type
- Journal article
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- Citation topics
- 9 Mathematics
- 9.50 Applied Statistics & Probability
- 9.50.649 BMO
- Web Of Science research areas
- Mathematics
- ESI research areas
- Mathematics