Hölder inequality for functions that are integrable with respect to bilinear maps - Blasco, O.; Calabuig, J. M. (MATHEMATICA SCANDINAVICA, 2008)
Let $(Ω, Σ, μ)$ be a finite measure space, $1\le p<∞$, $X$ be a Banach space $X$ and $B:X× Y → Z$ be a bounded bilinear map. We say that an $X$-valued function $f$ is $p$-integrable with respect to $B$ whenever $\sup_{\|y\|=1} \int_Ω \|B(f(w),y)\|^p\,dμ<∞$. We get an analogue to Hölder's inequality in this setting.