Riesz transform on locally symmetric spaces and Riemannian manifolds with a spectral gap

Bulletin des Sciences Mathématiques - Tập 134 - Trang 37-43 - 2010
Lizhen Ji1,2, Peer Kunstmann3, Andreas Weber4
1Center of Mathematical Sciences, Zhejiang University, Hangzhou, 310027, China
2Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA
3Institut für Analysis, Universität Karlsruhe (TH), Kaiserstr. 89-93, 76128 Karlsruhe, Germany
4Institut für Algebra und Geometrie, Universität Karlsruhe (TH), Kaiserstr. 89-93, 76128 Karlsruhe, Germany

Tài liệu tham khảo

Auscher, 2004, Riesz transform on manifolds and heat kernel regularity, Ann. Sci. École Norm. Sup. (4), 37, 911, 10.1016/j.ansens.2004.10.003 Bakry, 1985, Transformations de Riesz pour les semi-groupes symétriques, vol. 1123, 130 Bakry, 1989, The Riesz transforms associated with second order differential operators, vol. 17, 1 Borel, 1983, Laplacian and the discrete spectrum of an arithmetic group, Amer. J. Math., 105, 309, 10.2307/2374262 Brooks, 1981, The fundamental group and the spectrum of the Laplacian, Comment. Math. Helv., 56, 581, 10.1007/BF02566228 Buser, 1982, A note on the isoperimetric constant, Ann. Sci. École Norm. Sup. (4), 15, 213, 10.24033/asens.1426 Coulhon, 1999, Riesz transforms for 1⩽p⩽2, Trans. Amer. Math. Soc., 351, 1151, 10.1090/S0002-9947-99-02090-5 Donnelly, 1979, Pure point spectrum and negative curvature for noncompact manifolds, Duke Math. J., 46, 497, 10.1215/S0012-7094-79-04624-6 Doyle, 1988, On the bass note of a Schottky group, Acta Math., 160, 249, 10.1007/BF02392277 Ji, 2008, Pointwise bounds for L2 eigenfunctions on locally symmetric spaces, Ann. Global Anal. Geom., 34, 387, 10.1007/s10455-008-9116-x Lax, 1982, The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces, J. Funct. Anal., 46, 280, 10.1016/0022-1236(82)90050-7 Leuzinger, 2004, Critical exponents of discrete groups and L2-spectrum, Proc. Amer. Math. Soc., 132, 919, 10.1090/S0002-9939-03-07173-9 Mandouvalos, 2009, Spectrum of the Laplacian and Riesz transform on locally symmetric spaces, Bull. Sci. Math., 133, 134, 10.1016/j.bulsci.2008.04.005 Müller, 1987, Manifolds with Cusps of Rank One, Spectral Theory and L2-Index Theorem, vol. 1244 Strichartz, 1983, Analysis of the Laplacian on the complete Riemannian manifold, J. Funct. Anal., 52, 48, 10.1016/0022-1236(83)90090-3 Sturm, 1993, On the Lp-spectrum of uniformly elliptic operators on Riemannian manifolds, J. Funct. Anal., 118, 442, 10.1006/jfan.1993.1150 Taylor, 1989, Lp-estimates on functions of the Laplace operator, Duke Math. J., 58, 773, 10.1215/S0012-7094-89-05836-5 2008 Thurston Triebel, 1995 Weber, 2008, Heat kernel bounds, Poincaré series, and L2 spectrum for locally symmetric spaces, Bull. Austral. Math. Soc., 78, 73, 10.1017/S0004972708000488