L^{𝑝} estimates on functions of Markov operators

L$^{p}$ estimates on functions of Markov operators
HTML articles powered by AMS MathViewer

by Michel Marias PDF

Proc. Amer. Math. Soc. 130 (2002), 1533-1537 Request permission

We prove L$^{p}$ estimates for functions of Markov operators on a discrete measure space of superpolynomial volume growth.

References

G. Alexopoulos, On the mean distance of random walks on groups, Bull. Sci. Math. (2) 111 (1987), no. 2, 189–199. MR 903336
G. Alexopoulos, Spectral multipliers on discrete groups, Bull. London Math. Soc., to appear.
Thomas Keith Carne, A transmutation formula for Markov chains, Bull. Sci. Math. (2) 109 (1985), no. 4, 399–405 (English, with French summary). MR 837740
Jeff Cheeger, Mikhail Gromov, and Michael Taylor, Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds, J. Differential Geometry 17 (1982), no. 1, 15–53. MR 658471
R. I. Grigorchuck, Degrees of growth of finitely generated groups and the theory of invariant means, Math. USSR-Izv., 25, (1985), 259-300.
W. Hebisch and L. Saloff-Coste, Gaussian estimates for Markov chains and random walks on groups, Ann. Probab. 21 (1993), no. 2, 673–709. MR 1217561, DOI 10.1214/aop/1176989263
Michael E. Taylor, $L^p$-estimates on functions of the Laplace operator, Duke Math. J. 58 (1989), no. 3, 773–793. MR 1016445, DOI 10.1215/S0012-7094-89-05836-5
Nicholas Th. Varopoulos, Long range estimates for Markov chains, Bull. Sci. Math. (2) 109 (1985), no. 3, 225–252 (English, with French summary). MR 822826