JournalsrmiVol. 8, No. 3pp. 367–439

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

  • Guozhen Lu

    Wayne State University, Detroit, USA
Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications cover
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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.

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Guozhen Lu, Weighted Poincaré and Sobolev inequalities for vector fields satisfying Hörmander's condition and applications. Rev. Mat. Iberoam. 8 (1992), no. 3, pp. 367–439

DOI 10.4171/RMI/129