Abstract
We consider the K -interpolation methods involving slowly varying functions. We establish some reiteration formulae including so-called L or R limiting interpolation spaces as well as the R R , R L , L R , and L L extremal interpolation spaces. These spaces arise in the limiting situations. The proofs of most reiteration formulae are based on Holmstedt-type formulae. Applications to grand and small Lorentz spaces in critical cases are given.
Highlights
Let A ≔ ðA0, A1Þ be a compaTtible couple of Banach or quasiBanach spaces such that A0 A1 ≠ f0g
The proofs of most reiteration formulae are based on Holmstedt-type formulae
Is a collection of crucial definitions and statements building a base of the real interpolation methods involving slowly vpaartiybinlegcfouunpclteioonfs(.qIunatshi-e)Bfoalnloawchinsgp,alceetsAsu≡cðhAt0h,aAt 1AÞ0bTe aAc1o≠mf0g
Summary
Let A ≔ ðA0, A1Þ be a compaTtible couple of Banach or quasiBanach spaces such that A0 A1 ≠ f0g. The motivation for this work was the articles [6,7,8], where it has been shown that for some limiting combinations of parameters, new interpolation spaces are required. Fernández-Martínez and Signes work with the scale ðA0, A1Þθ,E,b of interpolation spaces based on the family of rearrangement invariant Banach function spaces E. They have introduced and studied this rich scale in [2, 9].
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