Sharp estimates of the Jacobi heat kernel
Journal article, 2013

The heat kernel associated with the setting of the classical Jacobi polynomials is defined by an oscillatory sum which cannot be computed explicitly, in contrast to the situation for the two other classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters above -1/2. As an application of the upper bound obtained, we show that the maximal operator of the multi-dimensional Jacobi heat semigroup satisfies a weak type (1; 1) inequality. We also obtain sharp estimates of the Poisson-Jacobi kernel.

Jacobi polynomial

Poisson-Jacobi kernel

Jacobi heat kernel

Jacobi expansion

Jacobi semigroup

maximal operator

Author

Adam Nowak

Polish Academy of Sciences

Peter Sjögren

University of Gothenburg

Chalmers, Mathematical Sciences, Mathematics

Studia Mathematica

0039-3223 (ISSN)

Vol. 218 3 219-244

Subject Categories

Mathematical Analysis

DOI

10.4064/sm218-3-2

More information

Latest update

10/30/2018