2,280 research outputs found
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
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