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Михаил Дьяченко, M. Dyachenko (1999)
Двумерные классы Ватермана и $u$-сходимость рядов Фурье@@@Two-dimensional Waterman classes and $u$-convergence of Fourier seriesMatematicheskii Sbornik, 190
T. Akhobadze (2007)
On the convergence of generalized Cesàro means of trigonometric Fourier series. IIActa Mathematica Hungarica, 115
Izv. Akad. Nauk Armyan. SSR Ser. Mat., 21
Michael Schramm, D. Waterman (1982)
On the magnitude of Fourier coefficients, 85
Lawrence D'Antonio, D. Waterman (1997)
A SUMMABILITY METHOD FOR FOURIER SERIES OF FUNCTIONS OF GENERALIZED BOUNDED VARIATION, 17
D. Waterman (1976)
On the summability of Fourier series of functions of Λ-bounded variationStudia Mathematica, 55
Mat. Sb., 201
Александр Бахвалов, Alexandr Bakhvalov (2010)
О локальном поведении многомерной $Łambda$-вариации@@@On the local behaviour of the multidimensional $Łambda$-variationMatematicheskii Sbornik, 201
Dokl. Akad. Nauk, 437
D. Waterman (1972)
On convergence of Fourier sereies of functions of generalized bounded variation
Acta Math. Hungar., 115
AbstractFor certain classes of functions of Λ-bounded variation on [-π,π]{[-\pi,\pi]}, Waterman and D’Antonio constructed a sequence of summability kernels such that the corresponding integral means converge for any function from the class,but not for any function from a broader Λ′BV{\Lambda^{\prime}\mathrm{BV}} class.In our paper, we extend this result to the case of functions of two variables.
Georgian Mathematical Journal – de Gruyter
Published: Apr 1, 2021
Keywords: Generalized variation; summability kernels; 42B08; 26B30
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