<abstract xmlns="http://www.w3.org/1999/xhtml"> In this paper we present the concept of total κ-variation in the sense of Hardy-Vitali-Korenblum for a real function defined in the rectangle Iab⊂R2. We show that the space κBV(Iab, R) of real functions of two variables with finite total κ-variation is a Banach space endowed with the norm ||f||κ = |f (a)| + κTV( f, Iab). Also, we characterize the Nemytskij composition operator H that maps the space of functions of two real variables of bounded κ-variation κBV(Iab, R) into another space of a similar type and is uniformly bounded (or Lipschitzian or uniformly continuous).</abstract>

In this paper we present the concept of total κ-variation in the sense of Hardy-Vitali-Korenblum for a real function defined in the rectangle Iab⊂R2. We show that the space κBV(Iab, R) of real functions of two variables with finite total κ-variation is a Banach space endowed with the norm ||f||κ = |f (a)| + κTV( f, Iab). Also, we characterize the Nemytskij composition operator H that maps the space of functions of two real variables of bounded κ-variation κBV(Iab, R) into another space of a similar type and is uniformly bounded (or Lipschitzian or uniformly continuous).

The Bi-dimensional space of Korenblum and composition operator

Dpto. de Matemáticas y Física Universidad Nacional Experimental del Táchira San Cristóbal VENEZUELA

Escuela de Matemáticas Universidad Central de Venezuela Caracas VENEZUELA

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"The Bi-dimensional space of Korenblum and composition operator"}

In this paper we present the concept of total κ-variation in the sense of Hardy-Vitali-Korenblum for a real function defined in the rectangle Iab⊂R2. We show...

The Bi-dimensional space of Korenblum and composition operator

Published Online: Sep 25, 2015

Page range: 1 - 12

Received: Jun 08, 2013

DOI: https://doi.org/10.1515/tmmp-2015-0001

Keywords
κ-function, κ-variation, composition operator, regularization, Jensen equation, uniformly continuous and bounded operator

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

The Bi-dimensional space of Korenblum and composition operator

Published Online: Sep 25, 2015

Page range: 1 - 12

Received: Jun 08, 2013

DOI: https://doi.org/10.1515/tmmp-2015-0001

Keywordsκ-function, κ-variation, composition operator, regularization, Jensen equation, uniformly continuous and bounded operator

© 2015

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
κ-function, κ-variation, composition operator, regularization, Jensen equation, uniformly continuous and bounded operator