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

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

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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

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We give characterizations of Besov and Triebel-Lizorkin spaces B p q s ( Ω ) and F p q s ( Ω ) in smooth domains Ω ⊂ 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

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We study the ∂ ‾ -equation with Hölder estimates in q -convex wedges of ℂ n by means of integral formulas. If D ⊂ ℂ n is defined by some inequalities { ρ i ≤ 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 ∂ ‾ f = g for each continuous ( n , r ) -closed form g in D , n - q ≤ r ≤ n , with the following estimates: if d denotes the distance to the boundary of D and if d β g is bounded, then...

On some singular integral operatorsclose to the Hilbert transform

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

Colloquium Mathematicae

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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 . ∫ k ( x - y ) m ( x + y ) f ( y ) d y where k ( x ) = ∑ j ∈ ℤ 2 j φ j ( 2 j x ) for a family of functions φ j j ∈ ℤ satisfying conditions (1.1)-(1.3) given below.

A lifting theorem for locally convex subspaces of L 0

R. Faber (1995)

Studia Mathematica

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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 .