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On the integrability and $$L^ 1$$-convergence of double trigonometric series. (English) Zbl 0724.42015
The following problems for double cosine and sine series, whose coefficients form a null sequence of bounded variation, are investigated: (i) the series converges pointwise, (ii) the sum of the series is integrable, (iii) the series is the Fourier series of its sum, (iv) the series converges in $$L^ 1$$-norm.

##### MSC:
 42B05 Fourier series and coefficients in several variables 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
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