Summation of Multiple Fourier Series in Matrix Weighted Lp-Spaces

Abstract EN

This paper is concerned with rectangular summation of multiple Fourier series in matrix weighted Lp-spaces.

We introduce a product Muckenhoupt Ap condition for matrix weights W and prove that rectangular Fourier partial sums converge in the corresponding matrix weighted space Lp(?d;W), 1

The same result is shown to hold true for other summation methods such as Cesàro and summation with the Jackson kernel.