منابع مشابه
Lacunary Series in Qk Spaces
Under mild conditions on the weight function K we characterize lacunary series in the so-called QK spaces.
متن کاملA note on lacunary series in $mathcal{Q}_K$ spaces
In this paper, under the condition that $K$ is concave, we characterize lacunary series in $Q_{k}$ spaces. We improve a result due to H. Wulan and K. Zhu.
متن کاملa note on lacunary series in $mathcal{q}_k$ spaces
in this paper, under the condition that $k$ is concave, we characterize lacunary series in $q_{k}$ spaces. we improve a result due to h. wulan and k. zhu.
متن کاملLacunary Trigonometric Series. Ii
where E c [0, 1] is any given set o f positive measure and {ak} any given sequence of real numbers. This theorem was first proved by R. Salem and A. Zygmund in case of a -0, where {flk} satisfies the so-called Hadamard's gap condition (cf. [4], (5.5), pp. 264-268). In that case they also remarked that under the hypothesis (1.2) the condition (1.3) is necessary for the validity of (1.5) (cf. [4]...
متن کاملOn 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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ژورنال
عنوان ژورنال: Journal of Function Spaces and Applications
سال: 2008
ISSN: 0972-6802
DOI: 10.1155/2008/152321