Mean Convergence of Orthogonal Series

Authors: Jerome Newman, Walter Rudin - Proceedings of the American Mathematical Society 1952 cited by 31

j1 about the mean convergence of Fourier series in Lv spaces has been extended by Harry Pollard to series of classical orthogonal polynomials [2; 3; 4; S].In particular, it was shown that the Legendre expansion of a function f£Lv on ( -1, 1) converges in the mean of order ptof if 4/3<p<i, but that this is false for any p>4 (or l^p<4/3).The question of the status of the limiting values p=4 and p = 4/3 was raised but not settled by Pollard, and is repeated in the reviews