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- W1605419305 abstract "Consider the double trigonometric series whose coefficients satisfy conditions of bounded variation of order $(p, 0)$, $(0, p)$, and $(p, p)$ with the weight $(overline{|j|}, overline{|k|})^{p-1}$ for some $pgt 1$. The following properties concerning the rectangular partial sums of this series are obtained: (a) regular convergence; (b) uniform convergence; (c) weighted $L^r$-integrability and weighted $L^r$-convergence; and (d) Parseval's formula. Our results generalize Bary [1, p. 656], Boas [2, 3], Chen [6, 7], Kolmogorov [9], Marzug [10], M'oricz [11, 12, 13, 14], Ul'janov [15], Young [16], and Zygmund [17, p. 4]." @default.
- W1605419305 created "2016-06-24" @default.
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- W1605419305 date "1998-06-01" @default.
- W1605419305 modified "2023-09-25" @default.
- W1605419305 title "INTEGRABILITY, MEAN CONVERGENCE, AND PARSEVAL'S FORMULA FOR DOUBLE TRIGONOMETRIC SERIES" @default.
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- W1605419305 doi "https://doi.org/10.11650/twjm/1500406932" @default.
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