Bounded sequence-to-function generalized Hausdorff transformations

Georgakis (1988) obtained the norm of the transformation (Ta)(y) = Sigma(n=0)(infinity)(-y)(n)g((n))(y)/n ! a(n), y greater than or equal to 0 considered as an operator from the sequence space l(p), with weights Gamma(n + S + 1)/n ! to L-p [0,infinity), with weight y(s), s > -1. As corollaries he obtained inequality statements for Borel and generalized Abel transformations. He also obtained the best constants possible for several weighted norm inequalities of Hardy and Littlewood. In this paper Georgakis' results are extended to the Endl generalized Hausdorff matrices.