\(L\)-Correspondences: The inclusion \(L^ p (\mu, X)\subset L^ q (\upsilon, Y)\). (English) Zbl 0863.46021

Dawson, C. Bryan

Int. J. Math. Math. Sci. 19, No. 4, 723-726 (1996).

Summary: In order to study inclusions of the type \(L^p(\mu,X)\subset L^q(\upsilon,Y)\), we introduce the notion of an \(L\)-correspondence. After proving some basic theorems, we give characterizations of some types of \(L\)-correspondences and offer a conjecture that is similar to an equimeasurability theorem.

MSC:

46E30	Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
46E40	Spaces of vector- and operator-valued functions
46B99	Normed linear spaces and Banach spaces; Banach lattices

Keywords:

Lebesgue-Bochner spaces; measurable point mapping; inclusions; \(L\)-correspondence; equimeasurability theorem