Riesz transforms for Jacobi expansions

We define and study Riesz transforms and conjugate Poisson integrals associated with multi-dimensional Jacobi expansions.Comment: 24 pages; the paper will appear in J. Anal. Math. (2008

Sharp estimates of the spherical heat kernel

We prove sharp two-sided global estimates for the heat kernel associated with a Euclidean sphere of arbitrary dimension. This solves a long-standing open problem.Comment: 9 pages, to appear in J. Math. Pures Appl. (9

Genuinely sharp heat kernel estimates on compact rank-one symmetric spaces, for Jacobi expansions, on a ball and on a simplex

We prove genuinely sharp two-sided global estimates for heat kernels on all compact rank-one symmetric spaces. This generalizes the authors' recent result obtained for a Euclidean sphere of arbitrary dimension. Furthermore, similar heat kernel bounds are shown in the context of classical Jacobi expansions, on a ball and on a simplex. These results are more precise than the qualitatively sharp Gaussian estimates proved recently by several authors.Comment: 16 page

The multi-dimensional pencil phenomenon for Laguerre heat-diffusion maximal operators

We investigate in detail the mapping properties of the maximal operator associated with the heat-diffusion semigroup corresponding to expansions with respect to multi-dimensional standard Laguerre functions.Comment: 30 pages with 1 figure. This paper was published as Preprint 2007:35, Department of Mathematical Sciences, Chalmers University of Technology and University of Gothenbur