Spectrum of the Cesàro Operator on the Ultradifferentiable Function Spaces $${\mathcal E}_\omega ({\mathbb {R}}_+)$$

We characterize the boundedness and compactness of the extended Cesàro operator Tg from H∞ to the mixed norm space and Bloch-type space (or little Bloch-type space), where g is a given holomorphic function in the unit ball of Cn and Tg is defined by .

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On the continuous Cesàro operator in certain function spaces

Positivity ◽

10.1007/s11117-014-0321-5 ◽

2015 ◽

Vol 19 (3) ◽

pp. 659-679 ◽

Cited By ~ 4

Author(s):

Angela A. Albanese ◽

José Bonet ◽

Werner J. Ricker

Keyword(s):

Function Spaces ◽

Cesàro Operator ◽

Cesaro Operator

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Correction to: Fine spectra of the discrete generalized Cesàro operator on Banach sequence spaces

Monatshefte für Mathematik ◽

10.1007/s00605-020-01401-y ◽

2020 ◽

Author(s):

Yoshihiro Sawano ◽

Saad R. El-Shabrawy

Keyword(s):

Sequence Spaces ◽

Cesàro Operator ◽

Banach Sequence Spaces ◽

Cesaro Operator ◽

Banach Sequence

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Generalized Cesáro operator on BMOA space

The Journal of Analysis ◽

10.1007/s41478-020-00266-6 ◽

2020 ◽

Author(s):

Sunanda Naik

Keyword(s):

Cesàro Operator ◽

Cesaro Operator

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ESSENTIAL NORM OF EXTENDED CESÀRO OPERATORS FROM ONE BERGMAN SPACE TO ANOTHER

Bulletin of the Australian Mathematical Society ◽

10.1017/s0004972711003108 ◽

2011 ◽

Vol 85 (2) ◽

pp. 307-314 ◽

Cited By ~ 1

Author(s):

ZHANGJIAN HU

Keyword(s):

Unit Ball ◽

Bergman Space ◽

Holomorphic Functions ◽

Essential Norm ◽

Normal Weight ◽

Cesàro Operator ◽

Radial Derivative ◽

Image Position ◽

Cesaro Operator

AbstractLet Ap(φ) be the pth Bergman space consisting of all holomorphic functions f on the unit ball B of ℂn for which $\|f\|^p_{p,\varphi }= \int _B |f(z)|^p \varphi (z) \,dA(z)\lt +\infty $, where φ is a given normal weight. Let Tg be the extended Cesàro operator with holomorphic symbol g. The essential norm of Tg as an operator from Ap (φ) to Aq (φ) is denoted by $\|T_g\|_{e, A^p (\varphi )\to A^q (\varphi )} $. In this paper it is proved that, for p≤q, with 1/k=(1/p)−(1/q) , where ℜg(z) is the radial derivative of g; and for p>q, with 1/s=(1/q)−(1/p) .

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