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On Bi-dimensional Second Variation

Jurancy EreúJosé GiménezNelson Merentes — 2012

Commentationes Mathematicae

In this paper we present the concept of bounded second variation of a real valued function defined on a rectangle in 2 . We use Hardy-Vitali type technics in the plane in order to extend the classical notion of function of bounded second variation on intervals of . We introduce the class B V 2 ( I a b ) , of all functions of bounded second variation on a rectangle I a b 2 , and show that this class can be equipped with a norm with respect to which it is a Banach space. Finally, we present two results that show that integrals...

On Korenblum convex functions

Lorena Maria LopezJurancy EreúNelson Merentes — 2017

Commentationes Mathematicae

We introduce a new class of generalized convex functions called the κ -convex functions, based on Korenblum’s concept of κ -decreasing functions, where κ is an entropy (distortion) function. We study continuity and differentiability properties of these functions, and we discuss a special subclass which is a counterpart of the class of so-called d.c. functions. We characterize this subclass in terms of the space of functions of bounded second κ -variation, extending a result of F. Riesz. We also present...

On second κ -variation

Jurancy Josefina EreúLorena Maria LopezNelson José Merentes — 2016

Commentationes Mathematicae

We present the notion of bounded second κ -variation for real functions defined on an interval [ a , b ] . We introduce the class κ B V 2 ( [ a , b ] ) of all functions of bounded second κ -variation on [ a , b ] . We show several properties of this class and present a sufficient condition under which a composition operator acts between these spaces.

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