Boundedness in the mean of orthonormalized polynomials

For the polynomials {p_n(t)}₀, orthonormalized on [–1, 1] with weightp(t) = (1–t) (1+t)_v=1^m, we obtain necessary and sufficient conditions for boundedness of the sequences of norms: 1) 2) and 3) with the conditions that on [–1, 1] and (H,)^–1 L²(0, 2), where(H,) is the modulus of continuity in C(–1, 1) of function H.Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 759–770, May, 1973.