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

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
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