L. Maligranda (1997)
Collectanea Mathematica
Similarity:
We give characterizations of weights for which reverse inequalities of the Hölder type for monotone functions are satisfied. Our inequalities with general weights and with sharp constants complement previous results.
Gord Sinnamon (2002)
Publicacions Matemàtiques
Similarity:
A simple expression is presented that is equivalent to the norm of the Lp v → Lq u 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...
Jean Michel Rakotoson, Benoît Simon (1997)
Revista de la Real Academia de Ciencias Exactas Físicas y Naturales
Similarity:
Hans Heinig, Lech Maligranda (1995)
Studia Mathematica
Similarity:
Characterizations of weight functions are given for which integral inequalities of monotone and concave functions are satisfied. The constants in these inequalities are sharp and in the case of concave functions, constitute weighted forms of Favard-Berwald inequalities on finite and infinite intervals. Related inequalities, some of Hardy type, are also given.
Werner Clemens (2005)
Bollettino dell'Unione Matematica Italiana
Similarity:
We analyse mean values of functions with values in the boundary of a convex two-dimensional set. As an application, reverse integral inequalities imply exactly the same inequalities for the monotone rearrangement. Sharp versions of the classical Gehring lemma, the Gurov-Resetnyak theorem and the Muckenhoupt theorem are obtained.
Radko Mesiar, Jun Li, Endre Pap (2010)
Kybernetika
Similarity:
The integral inequalities known for the Lebesgue integral are discussed in the framework of the Choquet integral. While the Jensen inequality was known to be valid for the Choquet integral without any additional constraints, this is not more true for the Cauchy, Minkowski, Hölder and other inequalities. For a fixed monotone measure, constraints on the involved functions sufficient to guarantee the validity of the discussed inequalities are given. Moreover, the comonotonicity of the considered...
Gord Sinnamon (1994)
Studia Mathematica
Similarity:
The classical level function construction of Halperin and Lorentz is extended to Lebesgue spaces with general measures. The construction is also carried farther. In particular, the level function is considered as a monotone map on its natural domain, a superspace of . These domains are shown to be Banach spaces which, although closely tied to spaces, are not reflexive. A related construction is given which characterizes their dual spaces.
Gord Sinnamon (2001)
Publicacions Matemàtiques
Similarity:
An exact expression for the down norm is given in terms of the level function on all rearrangement invariant spaces and a useful approximate expression is given for the down norm on all rearrangement invariant spaces whose upper Boyd index is not one.