## $$L$$-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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