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- W2954675293 abstract "For the Gegenbauer weight function $w_{lambda}(t)=(1-t^2)^{lambda-1/2}$, $lambda>-1/2$, we denote by $VertcdotVert_{w_{lambda}}$ the associated $L_2$-norm, $$ Vert fVert_{w_{lambda}}:=Big(int_{-1}^{1}w_{lambda}(t)f^2(t),dtBig)^{1/2}. $$ We study the Markov inequality $$ Vert p^{prime}Vert_{w_{lambda}}leq c_{n}(lambda),Vert pVert_{w_{lambda}},qquad pin mathcal{P}_n, $$ where $mathcal{P}_n$ is the class of algebraic polynomials of degree not exceeding $n$. Upper and lower bounds for the best Markov constant $c_{n}(lambda)$ are obtained, which are valid for all $nin mathbb{N}$ and $lambda>-frac{1}{2}$." @default.
- W2954675293 created "2019-07-12" @default.
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- W2954675293 date "2017-02-20" @default.
- W2954675293 modified "2023-09-27" @default.
- W2954675293 title "Markov $L_2$ inequality with the Gegenbauer weight" @default.
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