On homogeneous Siegel domains of type II, we prove that under certain conditions, the subspace of a weighted -space (0 < p < ∞) consisting of holomorphic functions is reproduced by a weighted Bergman kernel. We also obtain some -estimates for weighted Bergman projections. The proofs rely on a generalization of the Plancherel-Gindikin formula for the Bergman space .
We show an explicit relation between the Chow form and the Grothendieck residue; and we clarify the role that the residue can play in the intersection theory besides its role in the division problem.
Our objective is to construct residue currents from Bochner-Martinelli type kernels; the computations hold in the non complete intersection case and provide a new and more direct approach of the residue of Coleff-Herrera in the complete intersection case; computations involve crucial relations with toroidal varieties and multivariate integrals of the Mellin-Barnes type.
The classical Riemann Mapping Theorem states that a nontrivial simply connected domain Ω in ℂ is holomorphically homeomorphic to the open unit disc 𝔻. We also know that "similar" one-dimensional Riemann surfaces are "almost" holomorphically equivalent. We discuss the same problem concerning "similar" domains in ℂⁿ in an attempt to find a multidimensional quantitative version of the Riemann Mapping Theorem
In this paper we obtain the -boundedness of Riesz transforms for the Dunkl transform for all .
We characterize the Schatten class weighted composition operators on Bergman spaces of bounded strongly pseudoconvex domains in terms of the Berezin transform.
Let be an open neighborhood of the origin in and let be complex analytic. Let be a generic linear form on . If the relative polar curve at the origin is irreducible and the intersection number is prime, then there are severe restrictions on the possible degree cohomology of the Milnor fiber at the origin. We also obtain some interesting, weaker, results when is not prime.
We consider separately radial (with corresponding group ) and radial (with corresponding group symbols on the projective space , as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the -algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the...