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arXiv · 1110.4253

General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series

Vladimir A. Mikhailets·Aleksandr A. Murach
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Abstract

We prove that the classical Menshov-Rademacher, Orlicz, and Tandori theorems remain true for orthogonal series given in the direct integrals of measurable collections of Hilbert spaces. In particular, these theorems are true for the spaces L_{2}(X,dμ;H) of vector-valued functions, where (X,μ) is an arbitrary measure space, and H is a real or complex Hilbert space of an arbitrary dimension.

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Vladimir A. Mikhailets, Aleksandr A. Murach. 2011-10-27. General forms of the Menshov-Rademacher, Orlicz, and Tandori theorems on orthogonal series. https://arxiv.org/abs/1110.4253

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