Generalization of a Mendeleeff problem

In this work for the polynomials
$$P_n(x)=a_0+\sum\limits^m_{k=1}x^{\gamma_k}\sum\limits_{v=1}^{\mu_k-1}a_{k,v}(\ln x)^v$$
with
$$||P_n ||_{L^2(0, 1)}=M, \mu_k\in N, k=1,2,\dots,m,~ \sum\limits_{k=1}^m\mu_k=n,$$
the problem of estimation of the coefficients $a$ is solved. Also the explicit form of the extremal polynom is given.