Hostname: page-component-788cddb947-wgjn4 Total loading time: 0 Render date: 2024-10-19T10:03:46.986Z Has data issue: false hasContentIssue false
  • English
  • Français

Integrability and L-convergence of multiple trigonometric series

Published online by Cambridge University Press:  17 April 2009

Chang-Pao Chen
Chang-Pao Chen
Affiliation:
Department of MathematicsNational Tsing Hua UniversityHsinchu Taiwan 30043, Republic of China
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is proved that under the following condition, the sum f of the double trigonometric series with coefficients cjk is integrable and the rectangular partial sums smn(f, x, y) converge to f in L1 norm:

.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 2 , April 1994 , pp. 333 - 339
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Fine, N.J., ‘On the Walsh functions’, Trans Amer. Math. Soc. 65 (1949), 372–414.CrossRefGoogle Scholar
[2]Móricz, F., ‘Convergence and integrability of double trigonometric series with coefficients of bounded variation’, Proc. Amer. Math. Soc. 102 (1988), 633–640.CrossRefGoogle Scholar
[3]Móricz, F., ‘On the integrability and L 1-convergence of double trigonometric series’, Studia. Math. 98 (1991), 203–225.CrossRefGoogle Scholar
[4]Móricz, F., Schipp, F. and Wade, W.R., ‘On the integrability of double Walsh series with special coefficients’, Michigan Math. J. 37 (1990), 191–201.CrossRefGoogle Scholar
[5]Schipp, F., Wade, W.R. and Simon, P., Walsh Series. An Introduction to Dyadic Harmonic Analysis (Akadémiai Kiadó, Budapest, 1990).Google Scholar
[6]Zygmund, A., Trigonometric Series (Cambridge Univ. Press, 1959).Google Scholar