Results 161 to 170 of about 5,540 (198)

Weighted Sobolev $$L^{p}$$ Estimates for Homotopy Operators on Strictly Pseudoconvex Domains with $$C^{2}$$ boundary

Journal of Geometric Analysis, 2019
We derive estimates in a weighted Sobolev space $W^{k,p}_{\mu}(D)$ for a homotopy operator on a bounded strictly pseudoconvex domain $D$ of $C^2$ boundary in ${\C}^n$.
Ziming Shi
semanticscholar   +1 more source

Boundary Invariants of Pseudoconvex Domains

The Annals of Mathematics, 1984
Let \(\Omega \subseteq {\mathbb{C}}^ n\) be a smoothly bounded pseudoconvex domain. A notion of multitype of a point \(P\in \partial \Omega\) is introduced. This term is defined in terms of directional derivatives of a defining function for \(\partial \Omega\).
openaire   +1 more source

Approximation on Pseudoconvex Domains

1980
Here we discuss some problems in approximation which are related to the problem of finding pseudoconvex neighborhoods. Since we omit various topics, we refer the reader to the articles of Birtel [4], Henkin and Chirka [16], and Wells [28].
Eric Bedford, John Erik Fornaess
openaire   +1 more source

Compactness of Hankel Operators with Symbols Continuous on the Closure of Pseudoconvex Domains

Integral equations and operator theory, 2018
Let $$\Omega $$Ω be a bounded pseudoconvex domain in $${\mathbb {C}}^2$$C2 with Lipschitz boundary or a bounded convex domain in $${\mathbb {C}}^n$$Cn and $$\phi \in C(\overline{\Omega })$$ϕ∈C(Ω¯) such that the Hankel operator $$H_{\phi }$$Hϕ is compact ...
Timothy G. Clos, Mehmet Çelik, Sonmez Sahutoglu   +2 more
semanticscholar   +1 more source

Hölder estimates for homotopy operators on strictly pseudoconvex domains with $$C^2$$C2 boundary

, 2017
We derive a new homotopy formula for a strictly pseudoconvex domain of $$C^2$$C2 boundary in $${\mathbf C}^n$$Cn by using a method of Lieb and Range and obtain estimates in Lipschitz spaces for the homotopy operators.
Xianghong Gong
semanticscholar   +1 more source

The Neumann Problem for the k-Cauchy–Fueter Complex over k-Pseudoconvex Domains in $$\mathbb {R}^4$$R4 and the $$L^2$$L2 Estimate

, 2017
The k-Cauchy–Fueter operator and complex are quaternionic counterparts of the Cauchy–Riemann operator and the Dolbeault complex in the theory of several complex variables, respectively. To develop the function theory of several quaternionic variables, we
Wei Wang
semanticscholar   +1 more source

A Domain with Non-plurisubharmonic Squeezing Function

, 2016
We construct a strictly pseudoconvex domain with smooth boundary whose squeezing function is not plurisubharmonic.
J. Fornæss, N. Shcherbina
semanticscholar   +1 more source

Carleson Measures on Weakly Pseudoconvex Domains

The Journal of Geometric Analysis
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Oka's principle in pseudoconvex domains

Complex Variables, Theory and Application: An International Journal, 2001
Let x be a Banach space with a Schauder basis, for which the hypothesis (X) in the sense of Lempert is satisfied, and Ω be a pseudoconvex domain in x. Let L be an Abelian complex Lie group. A L or eL be, respectively, the sheaves over Ω of germs of holomorphic or continuous mappings into L and be the canonical inclusion. Then the mapping induced by the
openaire   +1 more source

Pseudoconvex domains of semiregular type

1994
In this article we develop the geometric tools needed for obtaining more precise analytic information than known so-far on a relatively large class of bounded pseudoconvex domains Ω ⊂ ℂ n with C ∞-smooth boundary of finite type.
Klas Diederich, Gregor Herbort
openaire   +1 more source