A full characterization of multipliers for the strong $\rho$-integral in the euclidean space

Title:

A full characterization of multipliers for the strong $\rho$-integral in the euclidean space

Creator:

Tuo-Yeong, Lee

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c5684b68-dc20-4928-bccb-34562d3f157d
uuid:c5684b68-dc20-4928-bccb-34562d3f157d

Subject:

strong $\rho $-integral, multipliers, and dual space

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We study a generalization of the classical Henstock-Kurzweil integral, known as the strong $\rho $-integral, introduced by Jarník and Kurzweil. Let $(\mathcal S_{\rho } (E), \Vert \cdot \Vert )$ be the space of all strongly $\rho $-integrable functions on a multidimensional compact interval $E$, equipped with the Alexiewicz norm $\Vert \cdot \Vert $. We show that each element in the dual space of $(\mathcal S_{\rho } (E), \Vert \cdot \Vert )$ can be represented as a strong $\rho $-integral. Consequently, we prove that $fg$ is strongly $\rho $-integrable on $E$ for each strongly $\rho $-integrable function $f$ if and only if $g$ is almost everywhere equal to a function of bounded variation (in the sense of Hardy-Krause) on $E$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

657-674

Source:

Czechoslovak Mathematical Journal | 2004 Volume:54 | Number:3

Harvested from:

CDK

Metadata only:

false