Search

Abstract: We prove two results on the density of states of the discrete one dimensional quasi-periodic Schrödinger equation with an analytic potential and Diophantine frequencies in the perturbed regime. On the one hand, we prove that this function has the behavior of a Hölder- function. On the other, we show that the length of the gaps has a sub-exponential estimate which depends on its label given by the gap-labeling theorem. To cite this article: S. Hadj Amor, C. R. Acad. Sci. Paris, Ser. I 343 (2006). [Copyright &y& Elsevier]

In this Note, we study the behavior of the Hardy–Littlewood maximal function M on cusp manifolds in terms of the growth of the volume of the base space. In particular, we prove that for all 1 fixed, there exists such a manifold on which M is bounded on Lp for p>p0 but not for 1⩽p. To cite this article: H.-Q. Li, C. R. Acad. Sci. Paris, Ser. I 338 (2004). [Copyright &y& Elsevier]