This is a preview of subscription content, log in via an institution to check access.
References
Boas, R. P., jr.: Integrability of trigonometric series. I. Duke Math. J.18, 787–793 (1951).
—: Integrability of trigonometric series. III. Quart. J. Math. (Oxford) (2)3, 217–221 (1952).
Boas, R. P., jr.: Absolute convergence and integrability of trigonometric series. J. Rational Mechanics and Analysis5, 621–632 (1956).
Boas, R. P., jr.: Entire Functions, pp. 196–197. New York 1954.
Chen, Y. M.: On the integrability of functions defined by trigonometrical series. Math. Z.66, 9–12 (1956).
Chen, Y. M.: Some asymptotic properties of Fourier constants and integrability theorems. Math. Z.68, 227–244 (1957).
Edmonds, S. M.: The Parseval formulae for monotonic functions. II. Proc. Cambridge Phil. Soc.46, 231–248 (1950).
—: The Parseval formulae for monotonic functions. III. Proc. Cambridge Phil. Soc.46, 249–267 (1950).
Hardy, G. H., andJ. E. Littlewood: Elementary theorems concerning power series with positive coefficients and moment constants of positive functions. J. für Math.157, 141–158 (1927).
Hardy, G. H., andJ. E. Littlewood: Some new properties of Fourier constants. Math. Annalen97, 159–209 (1926).
Hardy, G. H., andJ. E. Littlewood: Some new properties of Fourier constants. J. London Math. Soc.6, 3–9 (1931).
Hardy, G. H., J. E. Littlewood andG. Pólya: Inequalities. Cambridge 1952.
Heywood, P.: Integrability theorems for power series and Laplace transforms. J. London Math. Soc.30, 302–310 (1955).
Heywood, P.: On the integrability of functions defined by trigonometric series. I. Quart. J. Math. (Oxford) (2)5, 71–76 (1954).
—: On the integrability of functions defined by trigonometric series. II. Quart. J. Math. (Oxford) (2)6, 77–79 (1955).
Izumi, S.: Some trigonometrical series. III. J. of Math. (Tokyo)1, 128–136 (1953).
Izumi, S.: Some trigonometrical series. XI. Tôhoku Math. J. (2)6, 73–77 (1954).
Izumi, S., andM. Satô: Integrability of trigonometrical series. I. Tôhoku Math. J. (2)6, 258–263 (1954).
Mulholland, H. P.: The generalization of certain inequality theorems involving powers. Proc. London Math. Soc. (2)33, 481–516 (1932).
Mulholland, H. P.: Concerning the generalization of the Young-Hausdorff theorem. Proc. London Math. Soc. (2)35, 257–293 (1933).
Salem, R.: Sur les séries de Fourier des fonctions de carré sommable. Comptes Rendus197, 1175–1176 (1933).
Salem, R.: Généralisation de certains lemmes de Van der Corput et applications aux séries trigonométriques. Comptes Rendus201, 470–472 (1935).
Sunouchi, G.: Integrability of trigonometrical series. J. of Math. (Tokyo)1, 99–103 (1953).
Sz.-Nagy, B.: Séries et intégrales de Fourier des fonctions monotones non bornées. Acta Sci. Math. (Szeged)13, 118–135 (1949).
Zygmund, A.: Trigonometrical Series. Warszawa-Lwów 1935.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Yung-Ming, C. Some further asymptotic properties of Fourier constants. Math Z 69, 105–120 (1958). https://doi.org/10.1007/BF01187395
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01187395