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Displaying similar documents to “Linear extension operators for restrictions of function spaces to irregular open sets”

Norm inequalities for potential-type operators.

Sagun Chanillo, Jan-Olov Strömberg, Richard L. Wheeden (1987)

Revista Matemática Iberoamericana

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The purpose of this paper is to derive norm inequalities for potentials of the form Tf(x) = ∫(Rn) f(y)K(x,y)dy,     x ∈ Rn, when K is a Kernel which satisfies estimates like those that hold for the Green function associated with the degenerate elliptic equations studied in [3] and [4].

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.

Hardy space estimates for multilinear operators (I).

Ronald R. Coifman, Loukas Grafakos (1992)

Revista Matemática Iberoamericana

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In this article we study bilinear operators given by inner products of finite vectors of Calderón-Zygmund operators. We find that necessary and sufficient condition for these operators to map products of Hardy spaces into Hardy spaces is to have a certain number of moments vanishing and under this assumption we prove a Hölder-type inequality in the H space context.