Discrete diffusion semigroups associated with Dunkl-Jacobi and exceptional Jacobi polynomials
\'A. P. Horv\'ath
TL;DR
This paper establishes weighted inequalities for maximal operators linked to discrete diffusion semigroups associated with exceptional Jacobi and Dunkl-Jacobi polynomials, extending previous results to more complex differential-difference operators.
Contribution
It introduces weighted inequality results for maximal operators related to new classes of discrete diffusion semigroups involving exceptional Jacobi and Dunkl-Jacobi polynomials.
Findings
Weighted inequalities for maximal operators are proved.
Extension of results from discrete heat semigroup to differential-difference operators.
Broader class of operators analyzed compared to previous work.
Abstract
Some weighted inequalities for the maximal operator with respect to the discrete diffusion semigroups associated with exceptional Jacobi and Dunkl-Jacobi polynomials are given. This setup allows to extend the corresponding results obtained for discrete heat semigroup recently to richer class of differential-difference operators.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Mathematical Analysis and Transform Methods · Mathematical functions and polynomials