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Boundedness of the Cesàro operator
on mixed norm spaces


Authors: Ji-huai Shi and Guang-bin Ren
Journal: Proc. Amer. Math. Soc. 126 (1998), 3553-3560
MSC (1991): Primary 47B38; Secondary 30D55
DOI: https://doi.org/10.1090/S0002-9939-98-04514-6
MathSciNet review: 1458263
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Abstract: In this note, the boundedness of the Cesàro operator on mixed norm space $H_{p,q}(\varphi )$, $ 0<p, q\le \infty $, is proved.


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

  • 1. A. Brown, P. R. Halmos and A. L. Shields, Cesàro operators, Acta Sci. Math. 26 (1965), 125-137. MR 32:4539
  • 2. T. M. Flett, The dual of an inequality of Hardy and Littlewood and some related inequalities, J. Math. Anal. Appl. 38 (1972), 746-765. MR 46:3799
  • 3. G. H. Hardy, Notes on some points in the integral calculus LXVI, Messenger of Math. 58 (1929), 50-52.
  • 4. M. Jie, The Cesàro operator is bounded on $H^{p}$ for $0<p<1$, Proc. Amer. Math. Soc. 116 (1992), 1077-1079. MR 93b:47064
  • 5. T. L. Kriete and D. Trutt, The Cesàro operator in $l^{2}$ is subnormal, Amer. J. Math. 93 (1971), 215-225. MR 43:6744
  • 6. J. H. Shi, Inequalities for the integral means of holomorphic functions and their derivatives in the ball of $C^{n}$, Trans. Amer. Math. Soc. 328 (1991), 619-637. MR 92c:32004
  • 7. A. G. Siskakis, Composition semigroups and the Cesàro operators on $H^{p}$, J. London Math. Soc. (2) 36 (1987), 153-164. MR 89a:47048
  • 8. A. G. Siskakis, The Cesàro operator is bounded on $H^{1}$, Proc. Amer. Math. Soc. 110 (1990), 461-462. MR 90m:47050

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Additional Information

Ji-huai Shi
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
Email: shijh@math.ustc.edu.cn

Guang-bin Ren
Affiliation: Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People’s Republic of China
Email: rengb@math.ustc.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-98-04514-6
Keywords: Ces\`{a}ro operator, mixed norm spaces
Received by editor(s): January 30, 1997
Received by editor(s) in revised form: April 18, 1997
Additional Notes: This research was supported by the National Natural Science Foundation of China and the National Education Committee Doctoral Foundation
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1998 American Mathematical Society

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