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

Revista Matemática Iberoamericana (1992)

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

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topLu, 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 -

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