Spaces of Functions of Generalized Bounded Variation. II: Questions of Uniform Convergence of Fourier Series |
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Authors: | Berezhnoī E I |
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Institution: | (1) Yaroslavl' State University, Yaroslavl' |
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Abstract: | Tests are given for uniform convergence of Fourier series for spaces of functions of generalized bounded variation; along with the well-known tests (of Salem–Oskolkov–Young, Chanturiya, and Waterman) we suggest new tests. We show that the Waterman test for uniform convergence of Fourier series is strongest and unimprovable. We present a theorem on exact estimates for the Fourier coefficients for spaces of functions of bounded variation which contains classical results, improves several well-known results, and gives some new results. |
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