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The tensor BMO-property of the sequence of partial sums of a multiple Fourier series

V. A. Rodin


Abstract: A general assertion, relating the phenomenon of rectangular oscillation of the sequence of rectangular partial sums of a multiple Fourier series and the strong summability of that series, is established. For the sequence of rectangular partial sums of a multiple Fourier series an analog is obtained of the BMO-property of multiple Fourier series, related to the tensor product of these spaces.

UDC: 517.51

MSC: 42B08

Received: 31.08.1992

 English version: Russian Academy of Sciences. Sbornik. Mathematics, 1995, 80:1, 211–224

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