Weighted integrability of double trigonometric series
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- by Chang-Pao Chen and Xin-Rong Huang PDF
- Proc. Amer. Math. Soc. 127 (1999), 1463-1471 Request permission
Abstract:
We study the double trigonometric series whose coefficients $c_{jk}$ are such that $\sum _{j=-\infty }^\infty \sum _{k=-\infty }^\infty |c_{jk}|<\infty .$ Then its rectangular partial sums converge uniformly to some $f\in C(T^2)$. We give sufficient conditions for the Lebesgue integrability of $\{f(x,y)-f(x,0)-f(0,y)+f(0,0)\}\phi (x,y)$, where $\phi (x,y)=1/xy, 1/x$, or $1/y$. For certain cases, they are also necessary conditions. Our results extend those of Boas and Móricz from the one-dimensional to the two-dimensional series.References
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Additional Information
- Chang-Pao Chen
- Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China
- Email: cpchen@math.nthu.edu.tw
- Xin-Rong Huang
- Affiliation: Department of Mathematics, National Tsing Hua University, Hsinchu, Taiwan 30043, Republic of China
- Received by editor(s): September 1, 1997
- Published electronically: January 29, 1999
- Additional Notes: This research was supported by National Science Council, Taipei, R.O.C., under Grant #NSC 86-2115-M-007-012.
- Communicated by: Christopher D. Sogge
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1463-1471
- MSC (1991): Primary 42B99, 42A16
- DOI: https://doi.org/10.1090/S0002-9939-99-04661-4
- MathSciNet review: 1476123