Some Hardy-type integral inequalities involving functions of two independent variables
In this paper, we give some new generalizations to the Hardy-type integral inequalities for functions of two variables by using weighted mean operators S 1 : = S 1 w f and S 2 : = S 2 w f defined by S 1 ( x , y ) = 1 W ( x ) W ( y ) ∫ x 2 x ∫ y 2 y w ( t ) w ( s ) f ( t , s ) d s d t , and S 2 ( x ,...
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| Veröffentlicht in: | Positivity : an international journal devoted to the theory and applications of positivity in analysis 2021-07, Vol.25 (3), p.853-866 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | In this paper, we give some new generalizations to the Hardy-type integral inequalities for functions of two variables by using weighted mean operators
S
1
:
=
S
1
w
f
and
S
2
:
=
S
2
w
f
defined by
S
1
(
x
,
y
)
=
1
W
(
x
)
W
(
y
)
∫
x
2
x
∫
y
2
y
w
(
t
)
w
(
s
)
f
(
t
,
s
)
d
s
d
t
,
and
S
2
(
x
,
y
)
=
∫
x
2
x
∫
y
2
y
w
(
t
)
w
(
s
)
W
(
t
)
W
(
s
)
f
(
t
,
s
)
d
s
d
t
,
with
W
(
z
)
=
∫
0
z
w
(
r
)
d
r
f
o
r
z
∈
(
0
,
+
∞
)
,
where
w
is a weight function. |
|---|---|
| ISSN: | 1385-1292 1572-9281 |
| DOI: | 10.1007/s11117-020-00791-5 |