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On the Lebesgue summability of double trigonometric series |
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| Authors: | Mó nika Bagota |
| Affiliation: | a University of Szeged, Teacher's Training College, Boldogasszony sugárút 6, 6725 Szeged, Hungary b University of Szeged, Bolyai Institute, Aradi vértanúk tere 1, 6720 Szeged, Hungary |
| Abstract: | We recall that the Lebesgue summability of a single trigonometric series is defined in terms of the symmetric differentiability of the sum of the formally integrated trigonometric series in question. In this paper, we present another proof of the theorem given in Zygmund's monograph. Then we define the notion of Lebesgue summability of a double trigonometric series and extend the theorem of Fatou and Zygmund from single to double trigonometric series. |
| Keywords: | Formal integration of double trigonometric series Symmetric derivative and its extension to functions in two variables The Lebesgue method of summability |
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