Local approximations and intrinsic characterization of spaces of smooth functions on regular subsets of ℝn

By Pavel Shvartsman. 2006

55 citations recorded by the source corpus.

We give an intrinsic characterization of the restrictions of Sobolev $W^{k}_{p}$ (ℝn ), Triebel–Lizorkin $F^{s}_{pq}$(ℝn ) and Besov $B^{s}_{pq}$(ℝn ) spaces to regular subsets of ℝn via sharp maximal functions and local approximations. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/98f5d6302cd2fd3a1562d56d5689e209ed6772ef

How researchers see this paper

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In Applied Mathematics

1. Yuan Zhou
2. L. Ihnatsyeva
3. T. Heikkinen
4. Heli Tuominen
5. P. Hajłasz
6. Pekka Koskela
7. Dachun Yang
8. Renjin Jiang

In Numerical Analysis

1. L. Ihnatsyeva
2. T. Heikkinen
3. Heli Tuominen
4. Yuan Zhou

Citations in the corpus

• Measure Density and Extension of Besov and Triebel–Lizorkin Functions (2014, methodology): “The connection of the n-regularity condition, or, in other words, a measure density condition, and the extension property for Sobolev spaces is studied in [39] and in [14].”
• Sobolev embeddings, extensions and measure density condition (2008, background): “Keywords: Sobolev spaces; Sobolev embedding; Extension operator; Measure density condition”
• Fractional Sobolev extension and imbedding (2014, methodology): “To overcome the possible non-integrability, we improve the extension operator in [14, 24] by replacing the mean vale uX with the median value mu(X) defined in (2.”