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Embeddings of concave functions and duals of Lorentz spaces.

Gord Sinnamon (2002)

Publicacions Matemàtiques

A simple expression is presented that is equivalent to the norm of the Lpv → Lqu embedding of the cone of quasi-concave functions in the case 0 < q < p < ∞. The result is extended to more general cones and the case q = 1 is used to prove a reduction principle which shows that questions of boundedness of operators on these cones may be reduced to the boundedness of related operators on whole spaces. An equivalent norm for the dual of the Lorentz spaceΓp(v) = { f: ( ∫0∞ (f**)pv...

Existence criteria for positive solutions of a nonlinear difference inequality

Sui Cheng, Guang Zhang (2000)

Annales Polonici Mathematici

This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.

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