In this paper we characterize Bergman spaces with respect to double integral of the functions $|f(z) -f(w)|/|z-w|$, $|f(z) -f(w)|/rho(z,w)$ and $|f(z) -f(w)|/beta(z,w)$, where $rho$ and $beta$ are the pseudo-hyperbolic and hyperbolic metrics. We prove some necessary and sufficient conditions that implies a function to be in Bergman spaces.
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
Let T be the Toeplitz algebra on the Bergman space La(B, dv) of the unit ball in C. We show that the image of T in the Calkin algebra satisfies the double commutant relation: π(T ) = {π(T )}′′. This is a surprising result, for it is the opposite of what happens in the Hardy-space
In this paper we study the duality of the harmonic spaces on the annulus Ω = Ω1 \Ω − between two pseudoconvex domains with Ω− ⊂⊂ Ω1 in Cn and the Bergman spaces on Ω−. We show that on the annulus Ω, the space of harmonic forms for the critical case on (0, n−1)-forms is infinite d
Abstract We establish an embedding theorem for the weighted Bergman spaces induced by a positive Borel measure $$d\omega (y)dx$$ d ω ( y ) x with doubling property $$\omega (0,2t)\le C\omega (0,t)$$ 0 , 2 t ≤ C . The characterization is given in terms of Carleson squares on upper
Abstract Bounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to Lebesgue $$L^q_\nu L ν q , where $$0<q<p<\infty 0 < ∞ $$\omega belongs class "Equation missing" radial weights satisfying two-sided do