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On double cosine, sine, and Walsh series with monotone coefficients. (English) Zbl 0741.42010
The author has extended from one-dimensional to two-dimensional series the results of Hardy and Littlewood on the \(L^ r\)-integrability of the sum \(f\) and the results of Stechkin on \(L^ 1\)-integrability of the maximum partial sum \(M^*\) on the case of cosine and sine series with monotone coefficients. He also proves that the \(L^ r\)-integrability of \(f\) and \(M^*\) is essentially equivalent for \(r>1\) in the two- dimensional setting. He also extends some of his own results from one- dimensional to two-dimensional Walsh series.

42B05 Fourier series and coefficients in several variables
42C10 Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.)
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