Weighted Poincaré and Sobolev inequalites for vector fields satisfying Hörmander's condition and applications.

Guozhen Lu

Revista Matemática Iberoamericana (1992)

  • Volume: 8, Issue: 3, page 367-439
  • ISSN: 0213-2230

Abstract

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In this paper we mainly prove weighted Poincaré inequalities for vector fields satisfying Hörmander's condition. A crucial part here is that we are able to get a pointwise estimate for any function over any metric ball controlled by a fractional integral of certain maximal function. The Sobolev type inequalities are also derived. As applications of these weighted inequalities, we will show the local regularity of weak solutions for certain classes of strongly degenerate differential operators formed by vector fields.

How to cite

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Lu, Guozhen. "Weighted Poincaré and Sobolev inequalites for vector fields satisfying Hörmander's condition and applications.." Revista Matemática Iberoamericana 8.3 (1992): 367-439. <http://eudml.org/doc/39431>.

@article{Lu1992,
abstract = {In this paper we mainly prove weighted Poincaré inequalities for vector fields satisfying Hörmander's condition. A crucial part here is that we are able to get a pointwise estimate for any function over any metric ball controlled by a fractional integral of certain maximal function. The Sobolev type inequalities are also derived. As applications of these weighted inequalities, we will show the local regularity of weak solutions for certain classes of strongly degenerate differential operators formed by vector fields.},
author = {Lu, Guozhen},
journal = {Revista Matemática Iberoamericana},
keywords = {Análisis armónico; Campos vectoriales; Degradación; Desigualdades; Operadores diferenciales; Teoría de pesos; weighted Poincaré inequalities; Hörmander’s condition; Sobolev type inequalities; degenerate differential operators},
language = {eng},
number = {3},
pages = {367-439},
title = {Weighted Poincaré and Sobolev inequalites for vector fields satisfying Hörmander's condition and applications.},
url = {http://eudml.org/doc/39431},
volume = {8},
year = {1992},
}

TY - JOUR
AU - Lu, Guozhen
TI - Weighted Poincaré and Sobolev inequalites for vector fields satisfying Hörmander's condition and applications.
JO - Revista Matemática Iberoamericana
PY - 1992
VL - 8
IS - 3
SP - 367
EP - 439
AB - In this paper we mainly prove weighted Poincaré inequalities for vector fields satisfying Hörmander's condition. A crucial part here is that we are able to get a pointwise estimate for any function over any metric ball controlled by a fractional integral of certain maximal function. The Sobolev type inequalities are also derived. As applications of these weighted inequalities, we will show the local regularity of weak solutions for certain classes of strongly degenerate differential operators formed by vector fields.
LA - eng
KW - Análisis armónico; Campos vectoriales; Degradación; Desigualdades; Operadores diferenciales; Teoría de pesos; weighted Poincaré inequalities; Hörmander’s condition; Sobolev type inequalities; degenerate differential operators
UR - http://eudml.org/doc/39431
ER -

Citations in EuDML Documents

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  1. Marco Biroli, Umberto Mosco, Sobolev and isoperimetric inequalities for Dirichlet forms on homogeneous spaces
  2. Silvana Marchi, C 1 , α local regularity for the solutions of the p -Laplacian on the Heisenberg group. The case 1 + 1 5 < p ≤ 2
  3. Patrick Cattiaux, Arnaud Guillin, Deviation bounds for additive functionals of Markov processes
  4. Alexander Grigor'yan, Laurent Saloff-Coste, Stability results for Harnack inequalities
  5. Patrick Cattiaux, Arnaud Guillin, deviation bounds for additive functionals of markov processes
  6. Bruno Franchi, Piotr Hajłasz, How to get rid of one of the weights in a two-weight Poincaré inequality?
  7. Guozhen Lu, Richard Wheeden, High order representation formulas and embedding theorems on stratified groups and generalizations
  8. Bruno Franchi, Guozhen Lu, Richard L. Wheeden, Representation formulas and weighted Poincaré inequalities for Hörmander vector fields
  9. Francesco Borrello, Degenerate Elliptic Equations and Morrey Spaces
  10. Donatella Danielli, Nicola Garofalo, Duy-Minh Nhieu, Trace inequalities for Carnot-Carathéodory spaces and applications

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