Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

A study of $ \alpha$-variation. I


Author: F. W. Gehring
Journal: Trans. Amer. Math. Soc. 76 (1954), 420-443
MSC: Primary 27.2X
DOI: https://doi.org/10.1090/S0002-9947-1954-0064859-9
MathSciNet review: 0064859
Full-text PDF

References | Similar Articles | Additional Information

References [Enhancements On Off] (What's this?)

  • [1] L. S. Bosanquet, Note on the absolute summability $ (C)$ of a Fourier series, J. London Math. Soc. vol. 11 (1936) pp. 11-15.
  • [2] J. C. Burkill and F. W. Gehring, A scale of integrals from Lebesgue's to Denjoy's, Quarterly Journal vol. 4 (1953) pp. 210-220. MR 0057307 (15:204i)
  • [3] G. H. Hardy, Divergent series, Oxford, 1949. MR 0030620 (11:25a)
  • [4] G. H. Hardy and J. E. Littlewood, A convergence criterion for Fourier series, Math. Zeit. vol. 28 (1928) pp. 612-634. MR 1544980
  • [5] F. Hausdorff, Momentprobleme für ein endliches Intervall, Math. Zeit. vol. 16 (1923) pp. 220-248. MR 1544592
  • [6] E. R. Love, A generalization of absolute continuity, J. London Math. Soc. vol. 26 (1951) pp. 1-13. MR 0039791 (12:599a)
  • [7] J. A. Shohat and J. D. Tamarkin, The problem of moments, New York, 1943. MR 0008438 (5:5c)
  • [8] D. V. Widder, The Laplace transform, Princeton, 1946.
  • [9] N. Wiener, The quadratic variation of a function and its Fourier coefficients, Journal of Mathematics and Physics vol. 3 (1924) pp. 73-94.
  • [10] L. C. Young, An inequality of the Hölder type connected with Stieltjes integration, Acta Math. vol. 67 (1936) pp. 251-282. MR 1555421
  • [11] -, Inequalities connected with bounded $ p$-th power variation in the Wiener sense and with integrated Lipschitz conditions, Proc. London Math. Soc. (2) vol. 43 (1937) pp. 449-467.
  • [12] -, General inequalities for Stieltjes integrals and the convergence of Fourier series, Math. Ann. vol. 115 (1938) pp. 581-612. MR 1513204

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 27.2X

Retrieve articles in all journals with MSC: 27.2X


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1954-0064859-9
Article copyright: © Copyright 1954 American Mathematical Society

American Mathematical Society