Two-weight norm inequalities for the Cesàro means of generalized Hermite expansions (Q1772334)

Given a real number \(\mu> -1/2\), let \(\{H^{\{\mu\}}_n(x): n= 0,1,2,\dots\}\) be the system of the generalized Hermite polynomials with respect to the weight function \(|x|^{2\mu} e^{-x^2}\), \(-\infty< x< \infty\). Two-weight norm inequalities indicated in the title are proved. A weak boundedness inequality is also derived, which yields an almost everywhere convergence result.