3/16/2006

Sergey Tikhonov
Centre de Recerca Matematica

Convergence of trigonometric series

We discuss three new convergence criteria (for p=\infty, 1<p<\infty, and p=1) of belonging of sums of trigonometric series to L_p. One-dimensional and multi-dimensional cases are examined. We also study Hardy-Littlewood type theorem for multiple trigonometric and Walsh series in L_p with Muckenhoupt-type weights.