Norms of Certain Operators on Weighted $\ell_p$Spaces and Lorentz Sequence Spaces

摘要

The problem addressed is the exact determination of the norms of the classical Hilbert, Copson and averaging operators on weighted spaces and the corresponding Lorentz sequence spaces , with the power weighting sequence or the variant defined by . Exact values are found in each case except for the averaging operator with , for which estimates deriving from various different methods are obtained and compared.