Criteria for functions to be of Hardy class $H^{p}$
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- by Shinji Yamashita PDF
- Proc. Amer. Math. Soc. 75 (1979), 69-72 Request permission
Abstract:
Let f be holomorphic in the disk $|z| < 1$. 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 $p = 2$.References
- Peter L. Duren, Theory of $H^{p}$ spaces, Pure and Applied Mathematics, Vol. 38, Academic Press, New York-London, 1970. MR 0268655
- W. K. Hayman, Multivalent functions, Cambridge Tracts in Mathematics and Mathematical Physics, No. 48, Cambridge University Press, Cambridge, 1958. MR 0108586 N. Lusin, Sur une propriété des fonctions à carré sommable, Bull. Calcutta Math. Soc. 20 (1930), 139-154.
- G. Piranian and W. Rudin, Lusin’s theorem on areas of conformal maps, Michigan Math. J. 3 (1955/56), 191–199. MR 83553, DOI 10.1307/mmj/1028990036
- A. Zygmund, Trigonometric series. 2nd ed. Vols. I, II, Cambridge University Press, New York, 1959. MR 0107776
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 75 (1979), 69-72
- MSC: Primary 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1979-0529215-8
- MathSciNet review: 529215