Norms of certain operators on weighted L-spaces and Lorentz sequence spaces.

Jameson, Graham J. O. and Lashkaripour, R. (2002) Norms of certain operators on weighted L-spaces and Lorentz sequence spaces. Journal of Inequalities in Pure and Applied Mathematics, 3 (1). pp. 1-17. ISSN 1443-5756

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Abstract

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.