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Integrability of power series


Author: Babu Ram
Journal: Proc. Amer. Math. Soc. 93 (1985), 255-261
MSC: Primary 41A58; Secondary 40A10, 42A16
DOI: https://doi.org/10.1090/S0002-9939-1985-0770532-7
MathSciNet review: 770532
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Abstract: The object of this paper is to obtain generalization of certain results of Jain [3] and Woyczynski [5] concerning integrability of power series.


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

  • [1] Y. M. Chen, Some asymptotic properties of Fourier constants and integrability theorems, Math. Z. 68 (1957), 227-244. MR 0092893 (19:1176a)
  • [2] -, Some further asymptotic properties of Fourier constants, Math. Z. 69 (1958), 105-120. MR 0096934 (20:3416)
  • [3] P. Jain, On the integrability of power series, Proc. Amer. Math. Soc. 42 (1974), 569-574. MR 0338666 (49:3430)
  • [4] B. Ram, Integrability theorems for power series, Colloq. Math. 31 (1974), 293-299. MR 0364935 (51:1189)
  • [5] W. A. Woyczynski, Positive coefficient elements of Hardy-Orlicz spaces, Colloq. Math. 21 (1970), 103-110. MR 0257722 (41:2371)
  • [6] A. Zygmund, Trigonometric series, Vol. I and II, Cambridge Univ. Press, 1968. MR 0236587 (38:4882)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0770532-7
Keywords: Orlicz function, $ {\Delta _\alpha }$ condition, Young function, quasi-monotone sequence, Jensen's inequality
Article copyright: © Copyright 1985 American Mathematical Society

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