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I am trying to make sense of some operators that come up on Buchholz and Summers' work on warped convolutions (two works on arxiv: 2008 and 2011). There, they work on a Hilbert space $H$ and on the ...

Given a Banach space $X$ and a measure space $(\Omega ,\mu )$, one says that a function $$ f:\Omega \to X $$ is Dunford integrable, or scalarly integrable if, for every $\varphi $ in the ...

I was wondering whether the following interpolation between $L^1$ and $L^2$ spaces is true: Let $f \in \mathbb{R}^n$ be such that $$ \alpha_1:= \int_{\mathbb{R}} \left\lVert f(x_1,\cdot,....\cdot) \...