The canonical injection of the Hardy-Orlicz space into the Bergman-Orlicz space
We study the canonical injection from the Hardy-Orlicz space into the Bergman-Orlicz space .
We study the canonical injection from the Hardy-Orlicz space into the Bergman-Orlicz space .
Let be a positive Borel measure on the complex plane and let with . We study the generalized Toeplitz operators on the Fock space . We prove that is bounded (or compact) on if and only if is a Fock-Carleson measure (or vanishing Fock-Carleson measure). Furthermore, we give a necessary and sufficient condition for to be in the Schatten -class for .
We introduce variable exponent Fock spaces and study some of their basic properties such as boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality. We also prove that under the global log-Hölder condition, the variable exponent Fock spaces coincide with the classical ones.
We consider Hilbert spaces which are counterparts of the de Branges-Rovnyak spaces in the context of the weighted Bergman spaces A2α, −1 < α < ∞. These spaces have already been studied in [8], [7], [5] and [1]. We extend some results from these papers