Abstract

The problem, posed by N.N. Luzin in 1915, on the convergence of trigonometric series to \({+}\infty\) on the set of positive measure, was solved by S.V. Konyagin in 1988. There naturally arises the question of N.N. Luzin for double trigonometric series. In the present paper the theorem is proved which contains the answer to this problem.

中文翻译：

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关于双功能级数收敛到$$ {\ mathbf {+}} \ boldsymbol {\ infty} $$的问题

摘要

NN Luzin在1915年提出的问题是，在一系列正度量上将三角级数收敛到\（{+} \ infty \），1988年SV Konyagin解决了这个问题。双三角级数。本文证明了定理，该定理包含了这个问题的答案。