A weighted \(L^ 2\) Markoff type inequality for classical weights (Q1804758)

The main result is an estimation of the weighted \(L_2\)-norm of \((\sqrt {A}/ w_m) (w_m P^{(m)})'\), for real algebraic polynomials \(P\) of degree at most \(n\), such that their weight \(L_2\)-norm with the same weight \(w_m\) is less than 1. Here \(w_m= A^m w\), where \(w\) is one of the classical weight functions (Jacobi, Laguerre, or Hermite weight), \(A(t)\) is constant (one) for Hermite weight, \(A(t) =t\) for Laguerre weight and \(A(t)= 1-t^2\) for Jacobi weight. The interval of integration corresponds to weights familiarly.