Disentanglement, multilinear duality and factorisation for nonpositive operators

In previous work we established a multilinear duality and factorisation theory for norm inequalities pointwise weighted geometric means of positive linear operators defined on normed lattices. this paper extend the reach first time to setting general spaces. The scope includes Fourier restriction-type inequalities. We also sharpen our operators. Our results all share common theme: estimates mean can be disentangled into quantitative each operator separately. concept disentanglement recurs throughout paper. methods used in - principally convex optimisation relied strongly positivity. contrast, use vector-valued reformulation disentanglement, properties (Rademacher-type) underlying spaces, probabilistic considerations related p-stable random variables.