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Weak-type operators and the strong fundamental lemma of real interpolation theory

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Krugljak N., Sagher Y., Shvartsman P.

Studia Mathematica

2005

tom 170

nr 2

173-201

We prove an interpolation theorem for weak-type operators. This is closely related to interpolation between weak-type classes. Weak-type classes at the ends of interpolation scales play a similar role to that played by BMO with respect to the $L^{p}$ interpolation scale. We also clarify the roles of some of the parameters appearing in the definition of the weak-type classes. The interpolation theorem follows from a K-functional inequality for the operators, involving the Calderón operator. The inequality was inspired by a K-J inequality approach developed by Jawerth and Milman. We show that the use of the Calderón operator is necessary. We use a new version of the strong fundamental lemma of interpolation theory that does not require the interpolation couple to be mutually closed.

Ograniczanie wyników

1 Studia Mathematica

1 Krugljak N.

1 Sagher Y.

1 Shvartsman P.

1 2005

Wyniki wyszukiwania

Weak-type operators and the strong fundamental lemma of real interpolation theory