Generalized Hilbert-Type Operator on Hardy Space - Naik, S.; Nath, P. K. (Communications in Mathematics and Applications, 2015)
If \(f\) be an analytic function on the unit disc \(D\) with Taylor series expansion \(f(z) = _n=0^∞ a_nz^n\), we consider the generalized Hilbert-type operator defined by \(H_a,b(f)(z)=_n=0^∞(_k=0^∞ Γ(n+a+1)Γ(n+k+1)Γ(n+1)Γ(n+k+b+2)a_k)z^n\) where \(Γ\) denotes the Gamma function and \(a, b C\). We find an upper bound for the norm of the generalized Hilbert-type operator on Hardy space.