Abstract
This paper deals with the weighted subelliptic p-Laplace operator constructed by Hörmander's vector fields:Lpu=divX(〈A(x)Xu(x),Xu(x)〉p−22A(x)Xu(x)), where u∈W1,p(U,w),1<p<Q,andA(x) is a bounded measurable and m×m symmetric matrix satisfyingλ−1w(x)2/p|ξ|2⩽〈A(x)ξ,ξ〉⩽λw(x)2/p|ξ|2,ξ∈Rm,w(x)∈Ap. We first prove existence of the modified Green function for Lp by virtue of Minty–Browder theorem and then existence of the Green function for Lp by checking the convergence of sequence of modified Green functions. Next, we derive upper bounds of the modified Green function for Lp by establishing the interpolation inequality in the weighted weak Lp spaces. Finally, the bounds of the Green function for Lp are also obtained by virtue of results for the modified Green function and the compact weighted embedding theorem.
Published Version
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