A theorem of Bosanquet states that the Fourier series of a 2?-periodic function of bounded variation is absolutely (C, :) summable. In this paper we give a quantitative version of Bosanquet's result.
Complementary Spaces and Multipliers of Double Fourier Series for Functions of Bounded Variation
✍ Scribed by S. Baron; E. Liflyand; U. Stadtmüller
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 110 KB
- Volume
- 250
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
Complementary spaces for Fourier series were introduced by G. Goes and generalized by M. Tynnov. In this paper we investigate a notion of complementary space for double Fourier series of functions of bounded variation. Various applications are given.
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