Sharp estimates of the Jacobi heat kernel
Artikel i vetenskaplig tidskrift, 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 semigroup
maximal operator
Jacobi polynomial
Jacobi expansion
Poisson-Jacobi kernel
Jacobi heat kernel