Sharp estimates of the Jacobi heat kernel

• Autorzy: Adam Nowak , Peter Sjögren
• Języki publikacji: EN

Abstrakty

EN

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 other two classical systems of orthogonal polynomials. We deduce sharp estimates giving the order of magnitude of this kernel, for type parameters α, β ≥ -1/2. Using quite different methods, Coulhon, Kerkyacharian and Petrushev recently also obtained such estimates. As an application of the bounds, 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.

Kategorie tematyczne

• 35K08: Heat kernel
• 42C05: Orthogonal functions and polynomials, general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 218
• Numer: 3
• Strony: 219-244

Daty

wydano

2013

Twórcy

autor

Adam Nowak

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland

autor

Peter Sjögren

• Mathematical Sciences, University of Gothenburg
• Mathematical Sciences, Chalmers University of Technology, SE-412 96 Göteborg, Sweden

Identyfikatory

DOI

10.4064/sm218-3-2