Kohn has proved that the Bergman projection associated to a smooth bounded domain D maps C°°(D) into C°°(D) when D is strictly pseudoconvex [11], and more generally, when the boundary of D satisfies certain geometric conditions [12]. Diederich and Fornaess [6] have shown that these conditions are satisfied when the boundary of D is real analytic and pseudoconvex. REMARKS. (A) Our proof of Theor...

We establish a weighted Lp norm estimate for the Bergman projection class of pseudoconvex domains. obtain an upper bound when domain is, example, bounded smooth strictly domain, finite type in C2, convex Cn, or decoupled Cn. The is related to Bekollé-Bonami constant and sharp. When smooth, bounded, pseudoconvex, we also lower norm. As additional application method proof, result that weak-type (...

Let (L, h) → (X,ω) be a compact toric polarized Kähler manifold of complex dimension n. For each k ∈ N, the fibre-wise Hermitian metric h on L induces a natural inner product on the vector space C∞(X,Lk) of smooth global sections of L by integration with respect to the volume form ω n n! . The orthogonal projection Pk : C∞(X,Lk) → H(X,L) onto the space H(X,L) of global holomorphic sections of L...

In this paper, we characterize the bonudedness and compactness of weighted composition operators from weighted Bergman spaces to weighted Bloch spaces. Also, we investigate weighted composition operators on weighted Bergman spaces and extend the obtained results in the unit ball of $mathbb{C}^n$.