PreprintCC BY 4.0arXiv
Weighted Bernstein-type inequalities on a trapezoidal domain
Abstract
We study weighted L2 Bernstein-type inequalities for algebraic polynomials on a trapezoidal domain. Using a parametrization by the unit square, we construct a natural symmetric second-order Sturm--Liouville operator and derive exact directional Bernstein inequalities with explicit constants. We also obtain strengthened estimates for the ordinary partial derivatives. Finally, we relate the corresponding boundary factors to Dini derivatives of the Siciak extremal function of the trapezoid.
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BibTeX
@misc{beberok2026weighted,
title = {{Weighted Bernstein-type inequalities on a trapezoidal domain}},
author = {Tomasz Beberok},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.33283},
eprint = {2609.33283},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.33283},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Weighted Bernstein-type inequalities on a trapezoidal domain
AU - Tomasz Beberok
PY - 2026
DA - 2026/09/27
PB - arXiv
DO - 10.48550/arxiv.2609.33283
UR - https://arxiv.org/abs/2609.33283
AB - We study weighted L^2 Bernstein-type inequalities for algebraic polynomials on a trapezoidal domain. Using a parametrization by the unit square, we construct a natural symmetric second-order Sturm--Liouville operator and derive exact directional Bernstein inequalities with explicit constants. We also obtain strengthened estimates for the ordinary partial derivatives. Finally, we relate the corresponding boundary factors to Dini derivatives of the Siciak extremal function of the trapezoid.
ER -