×

zbMATH — the first resource for mathematics

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.)
PDF BibTeX XML Cite
Full Text: DOI EuDML