Boundedness of $\mathcal{C}^{b,c}$ operators on Bloch spaces
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In this article, we consider the integral operator $\mathcal{C}^{b,c}$, which is defined as follows: $$ \mathcal{C}^{b,c}(f)(z)=\int_0^z \frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}dw, $$ 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 $\mathcal{C}^{b,c}$ operators on Bloch spaces.
Abstract
In this article, we consider the integral operator $\mathcal{C}^{b,c}$, which is defined as follows: $$ \mathcal{C}^{b,c}(f)(z)=\int_0^z \frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}dw, $$ 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 $\mathcal{C}^{b,c}$ operators on Bloch spaces.
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