On the representation of functions by series of Legandre polynomials in weighted $L_\mu^q [-1, 1]$ spaces

In this paper we construct the weighted $L_\mu^q[-1, 1], q \in[1, 4/3] \cup [4, +\infty)$ and Legandre series $\sum\limits_{k=1}^\infty c_p P_k(x) $, which is universal in $L_\mu^q [-1, 1]$.