On lacunary wavelet series

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On Lacunary Trigonometric Series.

1. Fundamental theorem. In a recent paper f I have proved the theorem that if a lacunary trigonometric series CO (1) X(a* cos nk6 + bk sin nk9) (nk+x/nk > q > 1, 0 ^ 0 ^ 2ir) 4-1 has its partial sums uniformly bounded on a set of 0 of positive measure, then the series (2) ¿(a*2 + bk2) k-l converges. The proof was based on the following lemma (which was not stated explicitly but is contained in ...

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Lacunary Trigonometric Series. Ii

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ژورنال

عنوان ژورنال: The Annals of Applied Probability

سال: 2000

ISSN: 1050-5164

DOI: 10.1214/aoap/1019737675