Displaying similar documents to “The $\bar {\partial }$-Neumann operator on Lipschitz $q$-pseudoconvex domains”

Peak functions on convex domains

Kolář, Martin

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Let Ω ⊂ ℂ n be a domain with smooth boundary and p ∈ ∂ Ω . A holomorphic function f on Ω is called a C k ( k = 0 , 1 , 2 , ⋯ ) peak function at p if f ∈ C k ( Ω ¯ ) , f ( p ) = 1 , and | f ( q ) | < 1 for all q ∈ Ω ¯ ∖ { p } . If Ω is strongly pseudoconvex, then C ∞ peak functions exist. On the other hand, J. E. Fornaess constructed an example in ℂ 2 to show that this result fails, even for C 1 functions, on a weakly pseudoconvex domain [Math. Ann. 227, 173-175 (1977; Zbl 0346.32026)]. Subsequently, E. Bedford and J. E. Fornaess showed that there is always a continuous peak function...

The pluricomplex Green function on some regular pseudoconvex domains

Gregor Herbort (2014)

Annales Polonici Mathematici

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Let D be a smooth bounded pseudoconvex domain in ℂⁿ of finite type. We prove an estimate on the pluricomplex Green function D ( z , w ) of D that gives quantitative information on how fast the Green function vanishes if the pole w approaches the boundary. Also the Hölder continuity of the Green function is discussed.

On some extremal problems in Bergman spaces in weakly pseudoconvex domains

Romi F. Shamoyan, Olivera R. Mihić (2018)

Communications in Mathematics

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We consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂ n based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces A α p in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.

On some new sharp embedding theorems in minimal and pseudoconvex domains

Romi F. Shamoyan, Olivera R. Mihić (2016)

Czechoslovak Mathematical Journal

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We present new sharp embedding theorems for mixed-norm analytic spaces in pseudoconvex domains with smooth boundary. New related sharp results in minimal bounded homogeneous domains in higher dimension are also provided. Last domains we consider are domains which are direct generalizations of the well-studied so-called bounded symmetric domains in ℂ n . Our results were known before only in the very particular case of domains of such type in the unit ball. As in the unit ball case, all our...