Generalized Cesaro operators on weighted Dirichlet spaces

Given a complex Borel measure eta is an element of M(D), we study the boundedness of the Cesaro-type operator C-eta given by C-eta(f)(z) = Sigma(infinity)(n=0)(integral(D) w(n)d eta(w))(Sigma(n)(k=0) a(k))z(n) where f(z) = Sigma(infinity)(n=0)a(n)z(n), acting on the weighted Dirichlet spaces D-rho consisting in functions f is an element of H(D) with Sigma(infinity)(n=0)|a(n)|(2)(n + 1)rho(n) < infinity where (rho(n)) is a sequence of positive real numbers. We get new estimates on Taylor coefficients of functions in the Dirichlet space D-0 and extend the results known for D-alpha and positive measures nu supported in [0, 1) to more general weights and general measures. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).