Let L=∑ j=1 m Xj^2 be a Hörmander sum of squares of vector fields in space R^n, where any Xj is homogeneous of degree 1 with respect to a family of non-isotropic dilations in space. In this paper we prove global estimates and regularity properties for L in the X-Sobolev spaces Wx^k,p(R^n), where X={X1,…,Xm}. In our approach, we combine local results for general Hörmander sums of squares, the homogeneity property of the Xj's, plus a global lifting technique for homogeneous vector fields.
Global estimates in Sobolev spaces for homogeneous Hörmander sums of squares.
S. Biagi;M. Bramanti
2021-01-01
Abstract
Let L=∑ j=1 m Xj^2 be a Hörmander sum of squares of vector fields in space R^n, where any Xj is homogeneous of degree 1 with respect to a family of non-isotropic dilations in space. In this paper we prove global estimates and regularity properties for L in the X-Sobolev spaces Wx^k,p(R^n), where X={X1,…,Xm}. In our approach, we combine local results for general Hörmander sums of squares, the homogeneity property of the Xj's, plus a global lifting technique for homogeneous vector fields.File in questo prodotto:
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