Best constants in reversed Hardy's inequalities for quasimonotone functions

Let f be a nonnegative measurable function on (0,infty) and define the operators (Hsb1f)(x)=x^{-1}intsb0sp xf and (Hsb2f)(x)=x^{-1}intsb xsp infty f. Then consider the inequalities (1) |xspalpha(Hsb if)|sb{Lsp p}le Csb1 |xspalpha f|sb{Lsp p} and (2) |xspalpha f|sb{Lsp p}ge Csb2 |xspalpha(Hsb if)|sb{Lsp p}, where Csb1, Csb2>0 are constants independent of f, 0