Bounded sequence-to-function generalized Hausdorff transformations
Bounded sequence-to-function generalized Hausdorff transformations
Georgakis (1988) obtained the norm of the transformation \begin{equation*}(Ta)(y) = \sum ^{\infty }_{n=0} (-y)^{n} \frac {g^{(n)}(y)}{n!} a_{n},\quad y\geq 0, \end{equation*} considered as an operator from the sequence space $\ell ^{p}$, with weights $\Gamma (n+s+1)/n!$ to $L^{p}[0{,}\infty )$, with weight $y^{s}, s>-1$. As corollaries he obtained inequality statements for Borel and …