Cesaro summability of multi-dimensional trigonometric-Fourier series

[摘要] The d-dimensional classical Hardy spaces H-p(T-d) are introduced and it is shown that the maximal operator of the Cesaro means of a distribution is bounded from H-p(T-d) to L(p)(T-d) ((2d + 1)/(2d + 2) < p less than or equal to infinity) and is of weak type (1, 1) provided that the supremum in the maximal operator is taken over a positive cone. As a consequence we obtain the summability result due to Marcinkievicz and Zygmund, more exactly, the Cesaro means of a function f is an element of L(1)(T-d) converge a.e. to the function in question, provided again that the limit is taken over a positive cone. Similar results for the (C, beta) summability are also formulated. (C) 1996 Academic Press, Inc.

[发布日期] 1996-12-01