Weighted integrability

of double trigonometric series

Authors:
Chang-Pao Chen and Xin-Rong Huang

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

Published electronically:
January 29, 1999

MathSciNet review:
1476123

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Abstract | References | Similar Articles | Additional Information

Abstract: We study the double trigonometric series whose coefficients are such that Then its rectangular partial sums converge uniformly to some . We give sufficient conditions for the Lebesgue integrability of , where , or . 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.

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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

DOI:
https://doi.org/10.1090/S0002-9939-99-04661-4

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

Article copyright:
© Copyright 1999
American Mathematical Society