Circular summation and localization of double trigonometric series

Author:
Leonard D. Berkovitz

Journal:
Trans. Amer. Math. Soc. **70** (1951), 323-344

MSC:
Primary 42.4X

DOI:
https://doi.org/10.1090/S0002-9947-1951-0040464-2

MathSciNet review:
0040464

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References | Similar Articles | Additional Information

**[1]**S. Bochner,*Summation of multiple Fourier series by spherical means*, Trans. Amer. Math. Soc. vol. 40 (1936) pp. 175-207. MR**1501870****[2]**G. H. Hardy,*The second theorem of consistency for summable series*, Proc. London Math. Soc. (2) vol. 15 (1916) pp. 72-88.**[3]**G. H. Hardy and Marcel Riesz,*The general theory of Dirichlet's series*, Cambridge, 1915.**[4]**C. N. Moore,*On the summability of double Fourier series of discontinuous functions*, Math. Ann. vol. 74 (1913) pp. 555-572. MR**1511782****[5]**K. Sokol-Sokolowski,*On trigonometric series conjugate to Fourier series in two variables*, Fund. Math. vol. 34 (1947) pp. 166-182. MR**0021619 (9:89c)****[6]**A. Zygmund,*Sur la theorie riemannienne des series trigonometriques*, Math. Zeit. vol. 24 (1926) pp. 47-104. MR**1544748****[7]**-,*Trigonometrical series*, Warsaw, 1935.

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DOI:
https://doi.org/10.1090/S0002-9947-1951-0040464-2

Article copyright:
© Copyright 1951
American Mathematical Society