Linear summability methods for expansions of functions in the classes $L^p_\mu$ $(1\leqslant p\leqslant\infty)$ in orthonormal systems of polynomial type

In this article, sufficient conditions are derived under which, for all $x\in E\subset[a,b]$ (or uniformly on some set $E_1\subset[a,b]$), the following relation holds:
$$ \lim_{n\to\infty}U_n(f,x,\Lambda)=f(x), $$
where the $U_n(f,x,\Lambda)$ are linear means of expansions of functions in the classes $L^p_\mu$ $(1\leqslant p\leqslant\infty)$ in orthonormal systems of polynomial type.