  Let $w_{\lambda}(t) := (1-t^2)^{\lambda-1/2}$, where $\lambda >
-\frac{1}{2}$, be the Gegenbauer weight function, let $\|\cdot\|_{w_{\lambda}}$
be the associated $L_2$-norm, $$
  \|f\|_{w_{\lambda}} = \left\{\int_{-1}^1 |f(x)|^2
w_{\lambda}(x)\,dx\right\}^{1/2}\,, $$ and denote by $\mathcal{P}_n$ the space
of algebraic polynomials of degree $\le n$.
  We study the best constant $c_n(\lambda)$ in the Markov inequality in this
norm $$
  \|p_n'\|_{w_{\lambda}} \le c_n(\lambda) \|p_n\|_{w_{\lambda}}\,,\qquad p_n
\in \mathcal{P}_n\,, $$ namely the constant $$ c_n(\lambda) := \sup_{p_n \in
\mathcal{P}_n} \frac{\|p_n'\|_{w_{\lambda}}}{\|p_n\|_{w_{\lambda}}}\,. $$ We
derive explicit lower and upper bounds for the Markov constant $c_n(\lambda)$,
which are valid for all $n$ and $\lambda$.
