Journal of the Australian Mathematical Society

Research Article

Some regularity estimates for convolution semigroups on a group of polynomial growth

Nick Dungeya1

a1 School of Mathematics, University fo New South Wales, Sydney 2052, Australia e-mail: dungey@maths.unsw.edu.au

Abstract

We study a convolution semigroup satisfying Gaussian estimates on a group G of polynomial volume growth. If Q is a subgroup satisfying a certain geometric condition, we obtain high order regularity estimates for the semigroup in the direction of Q. Applications to heat kernels and convolution powers are given.

(Received December 20 2002)

(Revised June 25 2003)

2000 Mathematics subject classification

  • primary 22E30;
  • 35B40