For a wide range of pairs mixed norm spaces such that one space is contained in another, we characterize all cases when contractive inequalities hold. In particular, this yields results for many weighted Bergman spaces. Some type are motivated by their applications Number Theory and Mathematical Physics.

The boundedness of the difference of two weighted composition operators from weighted Bergman spaces to weighted-type spaces in the unit ball are investigated in this paper.

We study when a weighted composition operator acting between different weighted Bergman spaces is bounded, resp. compact.

This paper extends the theory of Zen spaces (weighted Hardy/Bergman on right-hand half-plane) to Hilbert-space valued case, and describes multipliers them; it is shown that methods H∞ control can therefore be extended certain weighted L2 input output spaces. Next, case retarded delay systems with operator-valued transfer functions analysed, dependence structure determined by developing an exten...

We give a necessary and a sufficient condition for the boundedness of the Toeplitz product TF TG∗ on the vector valued Bergman space L 2 a(C ), where F and G are matrix symbols with scalar valued Bergman space entries. The results generalize those in the scalar valued Bergman space case [4]. We also characterize boundedness and invertibility of Toeplitz products TF TG∗ in terms of the Berezin t...

Let dA denote Lebesgue area measure on the unit disk D, normalized so that the measure of D equals 1. For α > −1, we denote by dAα the measure dAα(z) = (α + 1)(1 − |z|2)αdA(z). For 1 ≤ p < +∞, the space L(D, dAα) is a Banach space. The weighted Bergman space Aα is the closed subspace of analytic functions in the Hilbert space L(D, dAα). For each z ∈ D, the application:Lz : A 2 α −→ C is continu...

We introduce an integral-type operator, denoted by P φ , on the space of holomorphic functions on the unit ball B ⊂ C, which is an extension of the product of composition and integral operators on the unit disk. The operator norm of P φ from the weighted Bergman space A p α B to the Bloch-type space Bμ B or the little Bloch-type space Bμ,0 B is calculated. The compactness of the operator is cha...