Weighted anisotropic integral representations of holomorphic functions in the unit ball of .
Weighted Bergman kernel: asymptotic behavior, applications and comparison results
Inspired by the work of Engliš, we study the asymptotic behavior of the weighted Bergman kernel together with an application to the Lu Qi-Keng conjecture. Some comparison results between the weighted and the classical Bergman kernel are also obtained.
Weighted Bergman projections and tangential area integrals
Let Ω be a bounded strictly pseudoconvex domain in . In this paper we find sufficient conditions on a function f defined on Ω in order that the weighted Bergman projection belong to the Hardy-Sobolev space . The conditions on f we consider are formulated in terms of tent spaces and complex tangential vector fields. If f is holomorphic then these conditions are necessary and sufficient in order that f belong to the Hardy-Sobolev space .
Weighted Bernstein-Markov property in ℂⁿ
We study the weighted Bernstein-Markov property for subsets in ℂⁿ which might not be bounded. An application concerning approximation of the weighted Green function using Bergman kernels is also given.
Weighted composition operators and integral-type operators between weighted Hardy spaces on the unit ball.
Weighted composition operators between a weighted-type space and the Hardy space on the unit ball
This paper characterizes the boundedness and compactness of weighted composition operators between a weighted-type space and the Hardy space on the unit ball of ℂⁿ.
Weighted composition operators from generalized weighted Bergman spaces to weighted-type spaces.
Weighted composition operators from Zygmund spaces to Bloch spaces on the unit ball
Let H() denote the space of all holomorphic functions on the unit ball ⊂ ℂⁿ. Let φ be a holomorphic self-map of and u∈ H(). The weighted composition operator on H() is defined by . We investigate the boundedness and compactness of induced by u and φ acting from Zygmund spaces to Bloch (or little Bloch) spaces in the unit ball.
Weighted generalization of the Ramadanov's theorem and further considerations
We study the limit behavior of weighted Bergman kernels on a sequence of domains in a complex space , and show that under some conditions on domains and weights, weighed Bergman kernels converge uniformly on compact sets. Then we give a weighted generalization of the theorem given by M. Skwarczyński (1980), highlighting some special property of the domains, on which the weighted Bergman kernels converge uniformly. Moreover, we show that convergence of weighted Bergman kernels implies this property,...
Weighted integrals of holomorphic functions in the unit polydisc.
Weighted Lp estimates for the Cauchy-Riemann equation on convex domains of finite type.
Weighted pluripotential theory on compact Kähler manifolds
We introduce a weighted version of the pluripotential theory on compact Kähler manifolds developed by Guedj and Zeriahi. We give the appropriate definition of a weighted pluricomplex Green function, its basic properties and consider its behavior under holomorphic maps. We also develop a homogeneous version of the weighted theory and establish a generalization of Siciak's H-principle.
Weighted Sobolev spaces in complex ellipsoids
Weighted θ-incomplete pluripotential theory
Weighted pluripotential theory is a rapidly developing area; and Callaghan [Ann. Polon. Math. 90 (2007)] recently introduced θ-incomplete polynomials in ℂ for n>1. In this paper we combine these two theories by defining weighted θ-incomplete pluripotential theory. We define weighted θ-incomplete extremal functions and obtain a Siciak-Zahariuta type equality in terms of θ-incomplete polynomials. Finally we prove that the extremal functions can be recovered using orthonormal polynomials and we...
Weights in cohomology and the Eilenberg-Moore spectral sequence
We show that in the category of complex algebraic varieties, the Eilenberg–Moore spectral sequence can be endowed with a weight filtration. This implies that it degenerates if all spaces involved have pure cohomology. As application, we compute the rational cohomology of an algebraic -variety ( being a connected algebraic group) in terms of its equivariant cohomology provided that is pure. This is the case, for example, if is smooth and has only finitely many orbits. We work in the category...
Weil-Petersson Metric in the Moduli Space of Compact Polarized Kähler-Einstein Manifolds of Zero First Chern Class.
Weil's formulae and multiplicity
The integral representation for the multiplicity of an isolated zero of a holomorphic mapping by means of Weil’s formulae is obtained.
Werteverhalten holomorpher Funktionen auf Überlagerungen und zahlentheoretische Analogien.
Weyl calculus for complex and real symmetric domains
We define the Weyl functional calculus for real and complex symmetric domains, and compute the associated Weyl transform in the rank 1 case.
Weyl closure of hypergeometric systems.