On Bernstein Inequalities on the Unit Ball
Abstract
Two types of Bernstein inequalities are established on the unit ball in $${\mathbb {R}}^d$$ , which are stronger than those known in the literature. The first type consists of inequalities in $$L^p$$ norm for a fully symmetric doubling weight on the unit ball. The second type consists of sharp inequalities in $$L^2$$ norm for the Jacobi weight, which are established via a new self-adjoint form of the spectral operator that has orthogonal polynomials as eigenfunctions.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Mathematical functions and polynomials
Mathematical Inequalities and Applications
Publication details
- Journal / source
- Constructive Approximation
- Publisher
- Springer Science and Business Media LLC
- Publication date
- 10 June 2026
- Language
- EN