Korean J. Math. Vol. 30 No. 3 (2022) pp.467-474
DOI: https://doi.org/10.11568/kjm.2022.30.3.467

Boundedness of Cb,c operators on Bloch spaces

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Published: Sep 30, 2022
Keywords:
Generalized Ces\'aro operators, Bloch-type space, Compactness.
Mathematics Subject Classification:
30D05, 30H05, 33C05, 47B38, 44A35.

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Pankaj Kumar Nath
Department of Applied Sciences, Gauhati University, Assam 781014, India
Sunanda Naik
Department of Applied Sciences, Gauhati University, Assam 781014, India

Abstract

In this article, we consider the integral operator Cb,c, which is
defined as follows:
Cb,c(f)(z)=∫0zf(w)∗F(1,1;c;w)w(1−w)b+1−cdw,
where ∗ denotes the Hadamard/ convolution product of power series, F(a,b;c;z) is the classical
hypergeometric function with b,c>0,b+1>c and f(0)=0.
We investigate the boundedness of the Cb,c operators on Bloch spaces.



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