Year: 2016
Type: preprint
Abstract: Let $(A,\mathscr{A},μ)$ and $(B,\mathscr{B},ν)$ be probability spaces, let $\mathscr{F}$ be a sub-$σ$-algebra of the product $σ$-algebra $\mathscr{A}\times\mathscr{B}$, let $X$ be a Banach space, and let $1< p,q< \infty$. We obtain necessary and sufficient conditions in order that the conditional expectation with respect to $\mathscr{F}$ defines a bounded linear operator from $L^p(μ;L^q(ν;X))$ onto $L^p_{\mathscr{F}}(μ;L^q(ν;X))$, the closed subspace in $L^p(μ;L^q(ν;X))$ of all functions having a strongly $\mathscr{F}$-measurable representative.
Source: arXiv (Cornell University)
Authors: Lu, Qi, van Neerven, Jan
Institutions: Sichuan University, Delft University of Technology
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2408904431