- Tytuł:
- High order representation formulas and embedding theorems on stratified groups and generalizations
- Autorzy:
-
Lu, Guozhen
Wheeden, Richard - Powiązania:
- https://bibliotekanauki.pl/articles/1205994.pdf
- Data publikacji:
- 2000
- Wydawca:
- Polska Akademia Nauk. Instytut Matematyczny PAN
- Tematy:
-
Poincaré inequalities
doubling measures
stratified groups
polynomials
representation formulas
vector fields
embedding theorems - Opis:
- We derive various integral representation formulas for a function minus a polynomial in terms of vector field gradients of the function of appropriately high order. Our results hold in the general setting of metric spaces, including those associated with Carnot-Carathéodory vector fields, under the assumption that a suitable $L^1$ to $L^1$ Poincaré inequality holds. Of particular interest are the representation formulas in Euclidean space and stratified groups, where polynomials exist and $L^1$ to $L^1$ Poincaré inequalities involving high order derivatives are known to hold. We apply the formulas to derive embedding theorems and potential type inequalities involving high order derivatives.
- Źródło:
-
Studia Mathematica; 2000, 142, 2; 101-133
0039-3223 - Pojawia się w:
- Studia Mathematica
- Dostawca treści:
- Biblioteka Nauki
Artykuł