Absolute convergence of multiple Fourier series revisited (Q949897)

Let \(T^n\) be the \(n\)-dimensional torus and \(f\in L^1(T^n)\) for some \(p\), \(1<p\leq 2\). The paper contains, under suitable hypotheses concerning the smoothness of \(f\), some results related to the absolute convergence of the series \[ \sum_{m\in N^n} c_m| \hat{f}_m| ^r \] \((r\in(0,q),\;1/p+1/q=1)\). These result extend some classical and recent results on this argument.