Generalized Laplacians and multiple trigonometric series
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- by M. J. Kohn PDF
- Trans. Amer. Math. Soc. 181 (1973), 419-428 Request permission
Abstract:
V. L. Shapiro gave a $k$-variable analogue for Riemann’s theorem on formal integration of trigonometric series. This paper derives Shapiro’s results with weaker conditions on the coefficients of the series and extends the results to series which are Bochner-Riesz summable of larger order.References
- Salomon Bochner, Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. 40 (1936), no. 2, 175–207. MR 1501870, DOI 10.1090/S0002-9947-1936-1501870-1 R. Courant, Methods of mathematical physics. Vol. II: Partial differential equations, Interscience, New York, 1962. MR 25 #4216.
- M. J. Kohn, Spherical convergence and integrability of multiple trigonometric series on hypersurfaces, Studia Math. 44 (1972), 345–354. MR 344796, DOI 10.4064/sm-44-4-345-354
- Victor L. Shapiro, Circular summability $C$ of double trigonometric series, Trans. Amer. Math. Soc. 76 (1954), 223–233. MR 61688, DOI 10.1090/S0002-9947-1954-0061688-7
- A. Zygmund, Trigonometric series: Vols. I, II, Cambridge University Press, London-New York, 1968. Second edition, reprinted with corrections and some additions. MR 0236587
Additional Information
- © Copyright 1973 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 181 (1973), 419-428
- MSC: Primary 42A92
- DOI: https://doi.org/10.1090/S0002-9947-1973-0320627-3
- MathSciNet review: 0320627