Geodesic
High order representation formulas and embedding theorems on stratified groups and generalizations
Studia Mathematica, Tome 142 (2000) no. 2, pp. 101-133

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm-142-2-101-133
Keywords: Poincaré inequalities, doubling measures, stratified groups, polynomials, representation formulas, vector fields, embedding theorems

Guozhen Lu 1 ; Richard Wheeden 1

1 
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Guozhen Lu; Richard Wheeden. High order representation formulas and embedding theorems on stratified groups and generalizations. Studia Mathematica, Tome 142 (2000) no. 2, pp. 101-133. doi: 10.4064/sm-142-2-101-133

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