## Landau type theorem for Orlicz spaces.(English)Zbl 0738.46013

This paper contains a short and elementary proof of the following fact: If $$L^ m$$ is an Orlicz space generated by a convex (not necessarily finite-valued) function $$M$$ and $$g$$ is a measurable function such that $$fg\in L^ 1$$ for all $$f\in L^ M$$, then $$g\in L^{M*}$$, where $$M^*$$ is the conjugate (=complementary) function of $$M$$.
This proposition implies analogous theorems for some classes of nonlocally convex Orlicz spaces (over atomless or counting measures). Moreover, this paper contains an example of an Orlicz space $$L^ M$$, whose Köthe dual is not isomorphic to any space of the form $$L^{M*}(\nu)$$.

### MSC:

 4.6e+31 Spaces of measurable functions ($$L^p$$-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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### References:

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