The Cesàro operator is bounded on $H^ 1$
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- by Aristomenis G. Siskakis PDF
- Proc. Amer. Math. Soc. 110 (1990), 461-462 Request permission
Abstract:
The purpose of this note is to give a direct proof that the Cesàro operator is bounded on the Hardy space ${H^1}$.References
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G. H. Hardy, Notes on some points in the integral calculus LXVI, Messenger of Math. 58 (1929), 50-52.
- G. H. Hardy and J. E. Littlewood, Some properties of fractional integrals. II, Math. Z. 34 (1932), no. 1, 403–439. MR 1545260, DOI 10.1007/BF01180596
- Aristomenis G. Siskakis, Composition semigroups and the Cesàro operator on $H^p$, J. London Math. Soc. (2) 36 (1987), no. 1, 153–164. MR 897683, DOI 10.1112/jlms/s2-36.1.153
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 461-462
- MSC: Primary 47B38; Secondary 30D55
- DOI: https://doi.org/10.1090/S0002-9939-1990-1021904-9
- MathSciNet review: 1021904