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

Studia Mathematica (2000)

- Volume: 142, Issue: 2, page 101-133
- ISSN: 0039-3223

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topLu, Guozhen, and Wheeden, Richard. "High order representation formulas and embedding theorems on stratified groups and generalizations." Studia Mathematica 142.2 (2000): 101-133. <http://eudml.org/doc/216792>.

@article{Lu2000,

abstract = {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.},

author = {Lu, Guozhen, Wheeden, Richard},

journal = {Studia Mathematica},

keywords = {Poincaré inequalities; doubling measures; stratified groups; polynomials; representation formulas; vector fields; embedding theorems; representation formula; Poincaré inequality; embedding theorem; polynomial; stratified group; vector field; doubling measure; Carnot-Carathéodory vector fields},

language = {eng},

number = {2},

pages = {101-133},

title = {High order representation formulas and embedding theorems on stratified groups and generalizations},

url = {http://eudml.org/doc/216792},

volume = {142},

year = {2000},

}

TY - JOUR

AU - Lu, Guozhen

AU - Wheeden, Richard

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

JO - Studia Mathematica

PY - 2000

VL - 142

IS - 2

SP - 101

EP - 133

AB - 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.

LA - eng

KW - Poincaré inequalities; doubling measures; stratified groups; polynomials; representation formulas; vector fields; embedding theorems; representation formula; Poincaré inequality; embedding theorem; polynomial; stratified group; vector field; doubling measure; Carnot-Carathéodory vector fields

UR - http://eudml.org/doc/216792

ER -

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