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 | References | Similar Articles | Additional Information

Abstract: In this note, the boundedness of the Cesàro operator on mixed norm space , , is proved.

**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 for*, Proc. Amer. Math. Soc.**116**(1992), 1077-1079. MR**93b:47064****5.**T. L. Kriete and D. Trutt,*The Cesàro operator in 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*, Trans. Amer. Math. Soc.**328**(1991), 619-637. MR**92c:32004****7.**A. G. Siskakis,*Composition semigroups and the Cesàro operators on*, J. London Math. Soc. (2)**36**(1987), 153-164. MR**89a:47048****8.**A. G. Siskakis,*The Cesàro operator is bounded on*, 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