Alexopoulos, Georges Inégalités de Harnack paraboliques et transformées de Riesz sur les groupes de Lie résolubles à croissance polynomiale du volume. (Parabolic Harnack inequalities and Riesz transforms on solvable Lie groups of polynomial growth). (French) Zbl 0699.22014 C. R. Acad. Sci., Paris, Sér. I 309, No. 10, 661-662 (1989). Let Q be a connected solvable Lie group, not necessarily nilpotent, of polynomial volume growth. Let \(X_ 1,...,X_ n\) be left-invariant vector fields that generate the Lie algebra of Q through successive brackets and put \(L=-(X^ 2_ 1+...+X^ 2_ n)\). The author announces Harnack type inequalities for non-negative solutions of the equation \(((\partial /\partial t)+L)u=0\) and boundedness properties of the Riesz operators \(X_ kL^{-1/2}\), \(L^{-1/2}X_ k\), \(k=1,...,n\). Reviewer: E.J.Akutowicz Cited in 2 Documents MSC: 22E30 Analysis on real and complex Lie groups 22E25 Nilpotent and solvable Lie groups 31C05 Harmonic, subharmonic, superharmonic functions on other spaces Keywords:connected solvable Lie group; left-invariant vector fields; Lie algebra; Harnack type inequalities; Riesz operators PDFBibTeX XMLCite \textit{G. Alexopoulos}, C. R. Acad. Sci., Paris, Sér. I 309, No. 10, 661--662 (1989; Zbl 0699.22014)