Hölder inequality for functions that are integrable with respect to bilinear maps
Keyword(s):
Let $(\Omega, \Sigma, \mu)$ be a finite measure space, $1\le p<\infty$, $X$ be a Banach space $X$ and $B:X\times Y \to Z$ be a bounded bilinear map. We say that an $X$-valued function $f$ is $p$-integrable with respect to $B$ whenever $\sup_{\|y\|=1} \int_\Omega \|B(f(w),y)\|^p\,d\mu<\infty$. We get an analogue to Hölder's inequality in this setting.
1977 ◽
Vol 24
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pp. 129-138
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1985 ◽
Vol 8
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pp. 433-439
1991 ◽
Vol 14
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pp. 245-252
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1992 ◽
Vol 111
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pp. 531-534
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1978 ◽
Vol 21
(3)
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pp. 347-354
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1991 ◽
Vol 117
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pp. 299-303
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1974 ◽
Vol 26
(6)
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pp. 1390-1404
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1988 ◽
Vol 40
(3)
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pp. 610-632
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