Boundedness and compactness of the mean operator matrix on weighted Hardy spaces (Q429094)

Let \(\beta=\{\beta(n)\}\) be a sequence of positive numbers with \(\beta(0)=1\) and \(1<p<\infty\). Given the space of sequences \(f=\left\{ \widehat{f}(n) \right\} _{n=0}^{\infty}\) such that NEWLINE\[NEWLINE \| f\|^{p}=\|f\|_{\beta}^{p} =\sum_{n=0}^{\infty}\left| \widehat{f}(n) \right| ^{p}\beta(n) ^{p}<\infty,NEWLINE\]NEWLINE the authors investigate the boundedness and the compactness of the mean operator matrix acting on the weighted Hardy spaces.