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Generalized potential type operators on rearrangement invariant spaces. (English) Zbl 0938.45010

Brudnyi, Yuri (ed.) et al., Function spaces, interpolation spaces, and related topics. Proceedings of the workshop, Haifa, Israel, June 7-13, 1995. Ramat Gan: Bar-Ilan University/distr. by the American Mathematical Society, Isr. Math. Conf. Proc. 13, 161-171 (1999).
Summary: We consider an integral operator \(T\) whose kernel \(G(x,y)\) depends on the distance \(|x-y|\) and is unbounded as \(x\) and \(y\) (which are points in \(\mathbb{R}^n)\) approach each other. It is shown that \(T:E\to F\) continuously for certain choices of rearrangement invariant spaces \(E\) and \(F\). Special attention is paid to the case of Orlicz spaces.
For the entire collection see [Zbl 0919.00055].

MSC:

45P05 Integral operators
47G10 Integral operators
46B70 Interpolation between normed linear spaces
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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