Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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BOUNDEDNESS OF 𝓒b,c OPERATORS ON BLOCH SPACES

  • Received : 2022.01.03
  • Accepted : 2022.08.20
  • Published : 2022.09.30
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Abstract

In this article, we consider the integral operator 𝓒b,c, which is defined as follows: $${\mathcal{C}}^{b,c}(f)(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\frac{f(w)*F(1,1;c;w)}{w(1-w)^{b+1-c}}}dw,$$ 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 𝓒b,c operators on Bloch spaces.

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