1Department of Mathematics Luleå University of Technology SE-971 87 Luleå, Sweden 2Department of Mathematical Sciences Florida Atlantic University Boca Raton, FL 33431-0991, U.S.A. 3Department of Mathematics Technion–Israel Institute of Technology 32000 Haifa, Israel
Studia Mathematica, Tome 170 (2005) no. 2, pp. 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 ${\rm BMO}$
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.
Keywords:
prove interpolation theorem weak type operators closely related interpolation between weak type classes weak type classes ends interpolation scales play similar role played bmo respect interpolation scale clarify roles parameters appearing definition weak type classes interpolation theorem follows k functional inequality operators involving calder operator inequality inspired k j inequality approach developed jawerth milman calder operator necessary version strong fundamental lemma interpolation theory does require interpolation couple mutually closed
Affiliations des auteurs :
N. Krugljak
1
;
Y. Sagher
2
;
P. Shvartsman
3
1
Department of Mathematics Luleå University of Technology SE-971 87 Luleå, Sweden
2
Department of Mathematical Sciences Florida Atlantic University Boca Raton, FL 33431-0991, U.S.A.
3
Department of Mathematics Technion–Israel Institute of Technology 32000 Haifa, Israel
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author = {N. Krugljak and Y. Sagher and P. Shvartsman},
title = {Weak-type operators and the strong fundamental
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N. Krugljak; Y. Sagher; P. Shvartsman. Weak-type operators and the strong fundamental
lemma of real interpolation theory. Studia Mathematica, Tome 170 (2005) no. 2, pp. 173-201. doi: 10.4064/sm170-2-4
