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Displaying similar documents to “Hölder Type Estimates for the ∂ ¯ -equation in Strongly Pseudoconvex Domains”

Hölder and L estimates for the solutions of the ∂-equation in non-smooth strictly pseudoconvex domains.

Josep M. Burgués Badía (1990)

Publicacions Matemàtiques

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Let D be a bounded strict pseudoconvex non-smooth domain in C. In this paper we prove that the estimates in L and Lipschitz classes for the solutions of the ∂-equation with L-data in regular strictly pseudoconvex domains (see [2]) are also valid for D. We also give estimates of the same type for the ∂ in the regular part of the boundary of these domains.

Semi-global solutions of ∂ with L (1 ≤ p ≤ ∞) bounds on strongly pseudoconvex real hypersurfaces in C (n ≥ 3).

C. H. Chang, H. P. Lee (1999)

Publicacions Matemàtiques

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Let M be an open subset of a compact strongly pseudoconvex hypersurface {ρ = 0} defined by M = D × C ∩ {ρ = 0}, where 1 ≤ m ≤ n-2, D = {σ(z, ..., z) < 0} ⊂ C is strongly pseudoconvex in C. For ∂ closed (0, q) forms f on M, we prove the semi-global existence theorem for ∂ if 1 ≤ q ≤ n-m-2, or if q = n - m - 1 and f satisfies an additional “moment condition”. Most importantly, the solution operator satisfies L estimates for 1 ≤ p ≤ ∞ with p = 1 and ∞ included.

Continuity of plurisubharmonic envelopes

Nihat Gokhan Gogus (2005)

Annales Polonici Mathematici

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Let D be a domain in ℂⁿ. The plurisubharmonic envelope of a function φ ∈ C(D̅) is the supremum of all plurisubharmonic functions which are not greater than φ on D. A bounded domain D is called c-regular if the envelope of every function φ ∈ C(D̅) is continuous on D and extends continuously to D̅. The purpose of this paper is to give a complete characterization of c-regular domains in terms of Jensen measures.

Extension and restriction of holomorphic functions

Klas Diederich, Emmanuel Mazzilli (1997)

Annales de l'institut Fourier

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Strong pathologies with respect to growth properties can occur for the extension of holomorphic functions from submanifolds D ' of pseudoconvex domains D to all of D even in quite simple situations; The spaces A p ( D ' ) : = 𝒪 ( D ' ) ∩ L p ( D ' ) are, in general, not at all preserved. Also the image of the Hilbert space A 2 ( D ) under the restriction to D ' can have a very strange structure.

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...