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An Optimal Interpolation Theorem of Marcinkiewicz Type in Orlicz Spaces

✍ Scribed by Andrea Cianchi

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 352 KB
Volume: 153
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.1997.3193

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✦ Synopsis

An extension of the Marcinkiewicz interpolation theorem is proved, yielding a necessary and sufficient condition for every quasilinear operator, satisfying given endpoint estimates of weak type, to be bounded from an Orlicz space into another.

1998 Academic Press in the last three papers mentioned above. They provide conditions on functions A and B, ensuring that every quasi-linear operator of weak type ( p i , q i ), with p i q i , i=0, 1, be bounded between the Orlicz spaces L A and L B . Those conditions include certain monotonicity and growth assumptions on article no.

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✍ Toshitaka Matsumoto; Takayoshi Ogawa 📂 Article 📅 2010 🏛 John Wiley and Sons 🌐 English ⚖ 193 KB

## Abstract An abstract version of Besov spaces is introduced by using the resolvent of nonnegative operators. Interpolation inequalities with respect to abstract Besov spaces and generalized Lorentz spaces are obtained. These inequalities provide a generalization of Sobolev inequalities of logarit