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.
| Comments: | Added two examples for which the new inequalities are quantitatively stronger than classical ones |
| Subjects: | Classical Analysis and ODEs (math.CA) |
| MSC classes: | 33C45, 42C05, 42C10 |
| Cite as: | arXiv:2511.09713 [math.CA] |
| (or arXiv:2511.09713v2 [math.CA] for this version) | |
| https://doi.org/10.48550/arXiv.2511.09713 arXiv-issued DOI via DataCite |
From: Yuan Xu [view email]
[v1]
Wed, 12 Nov 2025 20:20:37 UTC (21 KB)
[v2]
Fri, 22 May 2026 10:54:36 UTC (22 KB)
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