Exact <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" id="d1e25" altimg="si12.svg"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:math> Bernstein–Markov inequality on the ball
نویسندگان
چکیده
It is proved in this short note that for any polynomial p of d variables and degree at most n we have the sharp Bernstein–Markov type inequality ∫Bd(1−|x|2)μ+1|∂p|2≤M∫Bd(1−|x|2)μ|p|2,μ>−1, with M=n(n+d+2μ) M=n(n+d+2μ)−d+1 if even or odd, respectively. Here Bd unit ball Rd ∂p stands gradient polynomial. The upper bounds are attained certain Jacobi polynomials.
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2022
ISSN: ['0021-9045', '1096-0430']
DOI: https://doi.org/10.1016/j.jat.2022.105795