A Jordan Sobolev extension domain

Pekka Koskela, Dachun Yang, Yuan Zhou

Type: Article

Publication Date: 2010-03-01

Citations: 6

DOI: https://doi.org/10.5186/aasfm.2010.3519

Abstract

Let 1 < q < 2. In this paper, we construct a Jordan domain G q ⊂ R 2 such that G q ∈ Ext p if and only if 1 ≤ p < q, and R 2 \ G q ∈ Ext s if and only if q/(q -1) < s ≤ ∞.Theorem 1.1.For each 1 < q < 2, there exists a Jordan domain G q ⊂ R

Locations

Annales Academiae Scientiarum Fennicae Mathematica - View - PDF
CiteSeer X (The Pennsylvania State University) - View - PDF

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Works Cited by This (7)

Action	Title	Year	Authors
+	Weakly Differentiable Functions: Sobolev Spaces and Functions of Bounded Variation	1989	William P. Ziemer
+	Extensions and Imbeddings	1998	Pekka Koskela
+	Weighted Inequalities for Fractional Integrals on Euclidean and Homogeneous Spaces	1992	Eric T. Sawyer Richard L. Wheeden
+	Sobolev embeddings, extensions and measure density condition	2008	Piotr Hajłasz Pekka Koskela Heli Tuominen
+	Weakly Differentiable Functions	1989	William P. Ziemer
+	None	1996	Stephen M. Buckley Pekka Koskela
+	Geometric Properties of Planar BV -Extension Domains	2009	Pekka Koskela Michele Miranda Nageswari Shanmugalingam