Abstract. In this paper we study the two-parameter family of generalized Ces?ro operators $\mathcal{P}^{b,c}$ on the space of Cauchy transforms $K$. In [cs], Siskasis and Cima obtained the boundedness of the Ces?ro operator and $\alpha $-Ces?ro operator on the space of Cauchy transforms. Motivated by this we obtain the boundedness of the operators $\mathcal{P}^{b,c}$ on $K$ for $b+1>c>0$ as well as an upper bound of its norm. Also an alternate method for boundedness of $\mathcal{P}^{b,c}$ has been obtained by finding the adjoint of $\mathcal{P}^{b,c}$.

DOI: 10.14232/actasm-016-542-6

AMS Subject Classification (1991): 33C05, 30E20, 30H99, 46E15, 47B38

Keyword(s): Gaussian hypergeometric function, boundedness, spaces of Cauchy transforms

Received August 12, 2016, and in final form October 11, 2016. (Registered under 42/2016.)