$C^k$-estimates for the $\overline{\partial }$-equation on concave domains of finite type

William Alexandre

Displaying similar documents to “ $C^{k}$ -estimates for the $\bar{\partial}$ -equation on concave domains of finite type”

Optimal Lipschitz estimates for the $\bar{\partial}$ equation on a class of convex domains

Viêt Anh Nguyên, El Hassan Youssfi (2003)

Annales de la Faculté des sciences de Toulouse : Mathématiques

Similarity:

Hölder a priori estimates for second order tangential operators on CR manifolds

Annamaria Montanari (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

On a real hypersurface $M$ in $ℂ^{n + 1}$ of class $C^{2, α}$ we consider a local CR structure by choosing $n$ complex vector fields $W_{j}$ in the complex tangent space. Their real and imaginary parts span a $2 n$ -dimensional subspace of the real tangent space, which has dimension $2 n + 1 .$ If the Levi matrix of $M$ is different from zero at every point, then we can generate the missing direction. Under this assumption we prove interior a priori estimates of Schauder type for solutions of a class of second order partial differential...

Intrinsic characterizations of distribution spaces on domains

V. Rychkov (1998)

Studia Mathematica

Similarity:

We give characterizations of Besov and Triebel-Lizorkin spaces $B_{p q}^{s} (Ω)$ and $F_{p q}^{s} (Ω)$ in smooth domains $Ω \subset ℝ^{n}$ via convolutions with compactly supported smooth kernels satisfying some moment conditions. The results for s ∈ ℝ, 0 < p,q ≤ ∞ are stated in terms of the mixed norm of a certain maximal function of a distribution. For s ∈ ℝ, 1 ≤ p ≤ ∞, 0 < q ≤ ∞ characterizations without use of maximal functions are also obtained.

Uniform estimates for the Cauchy-Riemann equation on $q$ -convex wedges

Christine Laurent-Thiébaut, Jurgen Leiterer (1993)

Annales de l'institut Fourier

Similarity:

We study the $\overline{\partial}$ -equation with Hölder estimates in $q$ -convex wedges of $ℂ^{n}$ by means of integral formulas. If $D \subset ℂ^{n}$ is defined by some inequalities ${ρ_{i} \leq 0}$ , where the real hypersurfaces ${ρ_{i} = 0}$ are transversal and any nonzero linear combination with nonnegative coefficients of the Levi form of the $ρ_{i}$ ’s have at least $(q + 1)$ positive eigenvalues, we solve the equation $\overline{\partial} f = g$ for each continuous $(n, r)$ -closed form $g$ in $D$ , $n - q \leq r \leq n$ , with the following estimates: if $d$ denotes the distance to the boundary of $D$ and if $d^{β} g$ is bounded, then...

Solution of the $\bar{\partial}$ -equation on non-smooth strictly $q$ -concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem

Gerd Schmalz (1991)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

On some singular integral operatorsclose to the Hilbert transform

T. Godoy, L. Saal, M. Urciuolo (1997)

Colloquium Mathematicae

Similarity:

Let m: ℝ → ℝ be a function of bounded variation. We prove the $L^{p} (ℝ)$ -boundedness, 1 < p < ∞, of the one-dimensional integral operator defined by $T_{m} f (x) = p . v . \int k (x - y) m (x + y) f (y) d y$ where $k (x) = \sum_{j \in ℤ} 2^{j} φ_{j} (2^{j} x)$ for a family of functions ${φ_{j}}_{j \in ℤ}$ satisfying conditions (1.1)-(1.3) given below.

A lifting theorem for locally convex subspaces of $L_{0}$

R. Faber (1995)

Studia Mathematica

Similarity:

We prove that for every closed locally convex subspace E of $L_{0}$ and for any continuous linear operator T from $L_{0}$ to $L_{0} / E$ there is a continuous linear operator S from $L_{0}$ to $L_{0}$ such that T = QS where Q is the quotient map from $L_{0}$ to $L_{0} / E$ .

Displaying similar documents to “ C k -estimates for the ∂ ¯ -equation on concave domains of finite type”

Optimal Lipschitz estimates for the ∂ ¯ equation on a class of convex domains

Hölder a priori estimates for second order tangential operators on CR manifolds

Intrinsic characterizations of distribution spaces on domains

Uniform estimates for the Cauchy-Riemann equation on q -convex wedges

Solution of the ∂ ¯ -equation on non-smooth strictly q -concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem

On some singular integral operatorsclose to the Hilbert transform

A lifting theorem for locally convex subspaces of L 0

Displaying similar documents to “ $C^{k}$ -estimates for the $\bar{\partial}$ -equation on concave domains of finite type”

Optimal Lipschitz estimates for the $\bar{\partial}$ equation on a class of convex domains

Uniform estimates for the Cauchy-Riemann equation on $q$ -convex wedges

Solution of the $\bar{\partial}$ -equation on non-smooth strictly $q$ -concave domains with Hölder estimates and the Andreotti-Vesentini separation theorem

A lifting theorem for locally convex subspaces of $L_{0}$