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Criteria for functions to be of Hardy class $ H\sp{p}$

Author: Shinji Yamashita
Journal: Proc. Amer. Math. Soc. 75 (1979), 69-72
MSC: Primary 30D55
MathSciNet review: 529215
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Abstract: Let f be holomorphic in the disk $ \vert z\vert < 1$. Two criteria (see (I) and (II)) for f to be of $ {H^2}$ are extended to the case of $ {H^p},0 < p < + \infty $, by the methods different from known ones for $ p = 2$.

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  • [1] Peter L. Duren, Theory of 𝐻^{𝑝} spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
  • [2] W. K. Hayman, Multivalent functions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 48, Cambridge University Press, Cambridge, 1958. MR 0108586
  • [3] N. Lusin, Sur une propriété des fonctions à carré sommable, Bull. Calcutta Math. Soc. 20 (1930), 139-154.
  • [4] G. Piranian and W. Rudin, Lusin’s theorem on areas of conformal maps, Michigan Math. J. 3 (1955–1956), 191–199. MR 0083553
  • [5] A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776

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Article copyright: © Copyright 1979 American Mathematical Society

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