Abstract
We prove several new families of Bernstein inequalities of two types on the simplex. The first type consists of inequalities in \(L^2\) norm for the Jacobi weight, some of which are sharp, and they are established via the spectral operator that has orthogonal polynomials as eigenfunctions. The second type consists of inequalities in \(L^p\) norm for doubling weight on the simplex. The first type is not necessarily a special case of the second type when \(d \ge 3\).
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Notes
We thank Andras Kroó for pointing out this characterization for equality.
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Communicated by Kamen Ivanov
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The second author was partially supported by Simons Foundation Grant #849676.
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Ge, Y., Xu, Y. Sharp Bernstein Inequalities on Simplex. Constr Approx (2024). https://doi.org/10.1007/s00365-024-09680-6
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DOI: https://doi.org/10.1007/s00365-024-09680-6