A simple expression is presented that is equivalent to the norm of the $L_v^p \to L_u^q$ embedding of the cone of quasi-concave functions in the case 0 < q < p < ∞ ...

A class of generalized convex functions, the hyperbolic-concave functions, is defined, and used to characterize the collection of Hardy-Littlewood maximal functions. These maximal functions and the ...