Tohoku Mathematical Journal

On the averages of Fourier-Stieltjes coefficients

Lawrence Gluck

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 26, Number 3 (1974), 371-384.

Dates
First available in Project Euclid: 4 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178241131

Digital Object Identifier
doi:10.2748/tmj/1178241131

Mathematical Reviews number (MathSciNet)
MR0361590

Zentralblatt MATH identifier
0303.42002

Subjects
Primary: 42A16: Fourier coefficients, Fourier series of functions with special properties, special Fourier series {For automorphic theory, see mainly 11F30}
Secondary: 42A40

Citation

Gluck, Lawrence. On the averages of Fourier-Stieltjes coefficients. Tohoku Math. J. (2) 26 (1974), no. 3, 371--384. doi:10.2748/tmj/1178241131. https://projecteuclid.org/euclid.tmj/1178241131


Export citation

References

  • [1] R. BELLMAN, A note on a theorem of Hardy on Fourier constants, Bull. Amer. Math. Soc, 50 (1944), 741-744.
  • [2] C. GEORGAKIS, On the arithmetic mean of Fourier-Stieltjes coefficients, Proc. Amer Math. Soc, 33 (1972), 477-484.
  • [3] G. GOES, Arithmetic means of Fourier-Stieltjes sine coefficients, Proc. Amer. Math Soc, 14 (1963), 10-11.
  • [4] G. H. HARDY, Notes on some points in the integral calculus, Messenger of Math., 5 (1929), 50-52.
  • [5] R. HUNT, On L(p, q) spaces, Lnseignement Math., XII (1966), 249-276
  • [6] M. AND S. IZUMI, On Hardy's theorem, Proc Japan. Acad., 44 (1968), 418-423
  • [7] T. KAWATA, Notes on Fourier series XII, on Fourier constants, Proc. Imp. Acad. Tokyo, 20 (1944), 218-222.
  • [8] M. KINUKAWA AND S. IGARI, Transformations of conjugate functions, Thoku Math. J., 13 (1961), 274-280.
  • [9] M. A. KRASNOSEL'SKII AND YA. B. RUTICKII, Convex Functions and Orlicz Spaces, trans by L. F. Boron, P. Noordhoff Ltd., Groningen, The Netherlands, 1961.
  • [10] C. T. Loo, A note on properties of Fourier constants, Amer. J. Math., 71 (1949), 269-282
  • [11] G. G. LORENTZ, Some new functional spaces, Ann. Math., 51 (1950), 37-55
  • [12] G. M. PETERSEN, Means of Fourier constants, Trans. Royal Soc. Canada, XLV, Serie 111 (1951), 32-38.
  • [13] G. SUNOUCHI, On Fourier constants, Proc Imp. Acad. Tokyo, 20 (1944), 542-544
  • [14] P. TURAN, On a trigonometrical sum, Annales de la Soc. Polon. de Math., 25 (1952), 155-161.
  • [15] S. WANG, On some theorems on conjugate functions, Scienta Sinica, vol. XIV, no. (1965), 507-520.
  • [16] A. ZYGMUND, Trigonometric Series I, II, Cambridge University Press, 1959