Interpolation of Marcinkiewicz spaces.
Copyright policy )Interpolation of Marcinkiewicz spaces.
For each non-negative concave function \(\phi\) (t), the Marcinkiewicz space \(M_{\phi}\) consists of all measurable functions f such that \((\phi (t))^{-1}\int^{t}_{0}f^*(s)ds\leq C\) for all \(t>0\) and some constant C. Interpolation spaces with respect to couples \((M_{\phi_ 0},M_{\phi_ 1})\) of such spaces are considered. It is shown that for certain choices of \(\phi_ 0\) and \(\phi_ 1\) these interpolation spaces can be characterized by a monotonicity property with respect to the K- functional, that is \((M_{\phi_ 0},M_{\phi_ 1})\) is a Caldéron couple.
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510.mathematics, interpolation spaces, Abstract interpolation of topological vector spaces, Calderón couple, Marcinkiewicz space, K-functional, Article, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
510.mathematics, interpolation spaces, Abstract interpolation of topological vector spaces, Calderón couple, Marcinkiewicz space, K-functional, Article, Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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