On some structural properties of Banach function spaces and boundedness of certain integral operators

Title:

On some structural properties of Banach function spaces and boundedness of certain integral operators

Creator:

Kopaliani, T. S.

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:8e842c67-e716-449f-9d89-f4fe3c69713f
uuid:8e842c67-e716-449f-9d89-f4fe3c69713f

Subject:

Banach function space, uniformly upper, uniformly lower $\ell $-estimate, and Hardy type operator

Type:

model:article and TEXT

Description:

In this paper the notions of uniformly upper and uniformly lower $\ell $-estimates for Banach function spaces are introduced. Further, the pair $(X,Y)$ of Banach function spaces is characterized, where $X$ and $Y$ satisfy uniformly a lower $\ell $-estimate and uniformly an upper $\ell $-estimate, respectively. The integral operator from $X$ into $Y$ of the form \[ K f(x)=\varphi (x) \int _0^x k(x,y)f(y)\psi (y)\mathrm{d}y \] is studied, where $k$, $\varphi $, $\psi $ are prescribed functions under some local integrability conditions, the kernel $k$ is non-negative and is assumed to satisfy certain additional conditions, notably one of monotone type.

Language:

English

Rights:

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

Coverage:

791-805

Source:

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

Harvested from:

CDK

Metadata only:

false