Gantmacher–Kreĭn theorem for 2 nonnegative operators in spaces of functions.
Motivated by some recent results by Li and Stević, in this paper we prove that a two-parameter family of Cesàro averaging operators is bounded on the Dirichlet spaces . We also give a short and direct proof of boundedness of on the Hardy space for 1 < p < ∞.
Let f be an analytic function on the unit disk . We define a generalized Hilbert-type operator by , where a and b are non-negative real numbers. In particular, for a = b = β, becomes the generalized Hilbert operator , and β = 0 gives the classical Hilbert operator . In this article, we find conditions on a and b such that is bounded on Dirichlet-type spaces , 0 < p < 2, and on Bergman spaces , 2 < p < ∞. Also we find an upper bound for the norm of the operator . These generalize...
We investigate the conjugate indicator diagram or, equivalently, the indicator function of (frequently) hypercyclic functions of exponential type for differential operators. This gives insights into growth conditions for these functions on particular rays or sectors. Our research extends known results in several respects.