On a problem of littlewood |
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Authors: | M Khazaradze |
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Institution: | (1) Faculty of Mechanics and Mathematics, I. Javakhishvili Tbilisi State University, 2, University St., 380043 Tbilisi, Republic of Georgia |
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Abstract: | The theorem on the tending to zero of coefficients of a trigonometric series is proved when theL
1-norms of partial sums of this series are bounded. It is shown that the analog of Helson's theorem does not hold for orthogonal series with respect to the bounded orthonormal system. Two facts are given that are similar to Weis' theorem on the existence of a trigonometric series which is not a Fourier series and whoseL
1-norms of partial sums are bounded. |
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Keywords: | 42A16 |
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