Measure Density and Extension of Besov and Triebel-Lizorkin Functions

Tutkimustuotos: Lehtiartikkeli

Tutkijat

  • Toni Heikkinen
  • Lizaveta Ihnatsyeva
  • Heli Tuominen

Organisaatiot

  • University of Jyväskylä

Kuvaus

We show that a domain is an extension domain for a Hajlasz-Besov or for a Hajlasz-Triebel-Lizorkin space if and only if it satisfies a measure density condition. We use a modification of the Whitney extension where integral averages are replaced by median values, which allows us to handle also the case 0 <p <1. The necessity of the measure density condition is derived from embedding theorems; in the case of Hajlasz-Besov spaces we apply an optimal Lorentz-type Sobolev embedding theorem which we prove using a new interpolation result. This interpolation theorem says that Hajlasz-Besov spaces are intermediate spaces between L-p and Hajlasz-Sobolev spaces. Our results are proved in the setting of a metric measure space, but most of them are new even in the Euclidean setting, for instance, we obtain a characterization of extension domains for classical Besov spaces B-p,q(s), 0 <s <1, 0 <p <infinity, 0 <q

Yksityiskohdat

AlkuperäiskieliEnglanti
Sivut334-382
Sivumäärä49
JulkaisuJournal of Fourier Analysis and Applications
Vuosikerta22
Numero2
TilaJulkaistu - huhtikuuta 2016
OKM-julkaisutyyppiA1 Julkaistu artikkeli, soviteltu

ID: 4688522