Summation of multiple Fourier series in matrix weighted \(L_p\)-spaces (Q355642)

The paper deals with the problem of convergence and summation of multiple Fourier series in matrix weighted \(L_p\) spaces. The summation of Fourier coefficients considered in this paper is rectangular. The main result is Theorem 12, where the author proved that the rectangular partial sums of the Fourier series for \(f\in L_p(T^d,W)\) \((1<p<\infty)\) converge to \(f\) in the \(L_p(T^d,W)\)-norm if and only if \(W\) is an \(AP_p\)-weight. Moreover, it happens if and only if the rectangular partial sums are summable in Cesàro or Jackson sense.