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, 1p<∞, 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 _\|y\|=1 _Ω \|B(f(w),y)\|^p dμ<∞. We get an analogue to Hölder’s inequality in this setting.