The Cesàro operator is bounded on 𝐻¹

Siskakis, Aristomenis G.

doi:10.1090/S0002-9939-1990-1021904-9

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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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

Notes on some points in the integral calculus

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