Sharp Bounds for the Generalized Hardy Operators

Abstract

We get the sharp bound for weak type $(1,1)$ inequality for $n$-dimensional Hardy operator. Moreover, the precise norms of generalized Hardy operators on the type of Campanato spaces are obtained. As applications, the corresponding norms of the Riemann-Liouville integral operator and $n$-dimensional Hardy operator are deduced.

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• Hardy's operator and normability of generalized Lorentz-Marcinkiewicz spaces, with sharp or weakly sharp constant estimation