Quantitative estimates in Beurling-Helson type theorems
Journal Article
·
· Sbornik. Mathematics
- Moscow State Institute of Electronics and Mathematics (Technical University), Moscow (Russian Federation)
We consider the spaces A{sub p}(T) of functions f on the circle T such that the sequence of Fourier coefficients f-hat={l_brace}f-hat(k), k element of Z{r_brace} belongs to l{sup p}, 1{<=}p<2. The norm in A{sub p}(T) is defined by ||f||{sub A{sub p}}=||f-hat||{sub l}{sup P}. We study the rate of growth of the norms ||e{sup i{lambda}{phi}|}|{sub A{sub p}} as |{lambda}|{yields}{infinity}, {lambda} element of R, for C{sup 1}-smooth real functions {phi} on T. The results have natural applications to the problem of changes of variable in the spaces A{sub p}(T). Bibliography: 17 titles.
- OSTI ID:
- 21592579
- Journal Information:
- Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 12 Vol. 201; ISSN 1064-5616
- Country of Publication:
- United States
- Language:
- English
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