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

Czechoslovak Mathematical Journal (2004)

- Volume: 54, Issue: 3, page 791-805
- ISSN: 0011-4642

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topKopaliani, T. S.. "On some structural properties of Banach function spaces and boundedness of certain integral operators." Czechoslovak Mathematical Journal 54.3 (2004): 791-805. <http://eudml.org/doc/30901>.

@article{Kopaliani2004,

abstract = {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.},

author = {Kopaliani, T. S.},

journal = {Czechoslovak Mathematical Journal},

keywords = {Banach function space; uniformly upper; uniformly lower $\ell $-estimate; Hardy type operator; Banach function space; uniformly upper and uniformly lower -estimate; Hardy type operator},

language = {eng},

number = {3},

pages = {791-805},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {On some structural properties of Banach function spaces and boundedness of certain integral operators},

url = {http://eudml.org/doc/30901},

volume = {54},

year = {2004},

}

TY - JOUR

AU - Kopaliani, T. S.

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

JO - Czechoslovak Mathematical Journal

PY - 2004

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 54

IS - 3

SP - 791

EP - 805

AB - 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.

LA - eng

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

UR - http://eudml.org/doc/30901

ER -

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