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Double trigonometric series with positive coefficients

Двойной тригонометрический ряд с положительными коэффициентами

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Abstract

We present necessary and sufficient conditions for double sine, sinecosine, cosine-sine and double cosine series in terms of coefficients that their sums belong to double Lipschitz classes. Some classical results on single trigonometric series and some new results of Fülöp [2] on double trigonometric series are extended.

Резюме

В работе устанавливаются необходимые и достаточные условия, выраженные в терминах козффициентов, для того чтобы суммы двойных синус-, синус-косинус, косинус-синус и двойных косинус рядов с этими козффициентами принадлежали двойным классам Липшица. Обобщаются некоторые известные классические результаты для одномерных рядов, а также более новые результаты Фюлоп [2] для двойных рядов.

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Authors and Affiliations

  1. Department of Mathematics, Hangzhou Normal University, Hangzhou, 310016, Zhejiang, China

    Dansheng Yu

  2. Department of Mathematics, Statistics and Computer Science, St. Francis Xavier University, Antigonish, Canada, B2G 2W5

    Dansheng Yu

Authors
  1. Dansheng Yu
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Correspondence to Dansheng Yu.

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Research of the author is supposed by AARMS of Canada and Hangzhou Normal University.

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Yu, D. Double trigonometric series with positive coefficients. Anal Math 35, 149–167 (2009). https://doi.org/10.1007/s10476-009-0205-2

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  • DOI: https://doi.org/10.1007/s10476-009-0205-2

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