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

• Autorzy: N. Krugljak , Y. Sagher , P. Shvartsman
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B70: Interpolation between normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 170
• Numer: 2
• Strony: 173-201

Daty

wydano

2005

Twórcy

autor

N. Krugljak

• Department of Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

autor

Y. Sagher

• Department of Mathematical Sciences, Florida Atlantic University, Boca Raton, FL 33431-0991, U.S.A.

autor

P. Shvartsman

• Department of Mathematics, Technion-Israel Institute of Technology, 32000 Haifa, Israel

Identyfikatory

DOI

10.4064/sm170-2-4