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High order representation formulas and embedding theorems on stratified groups and generalizations

100%

Lu G., Wheeden R. L.

Studia Mathematica

2000

tom 142

nr 2

101-133

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.

Ograniczanie wyników

1 Studia Mathematica

1 Lu G.

1 Wheeden R. L.

1 2000

Wyniki wyszukiwania

High order representation formulas and embedding theorems on stratified groups and generalizations