These notes are devoted to the analysis on a capacity space, with capacities as substitutes of measures in the study of function spaces. The goal is to extend to the associated function lattices some aspects of the theory of Banach function spaces, to show how the general theory can be applied to classical function spaces such as Lorentz spaces, and to complete the real interpolation theory for these spaces included in Cerdà (J Math Anal Appl 304: 2005) and Cerdà et al. (AMS Contemp Math 445:49-55, 2007). Mathematics Subject Classification (2000) Primary 46E30; Secondary 46B70 · 46M35 · 28A12Keywords Capacity · Lorentz spaces · Interpolation IntroducctionThe purpose of this paper is to present some basic developments connected with properties of function spaces defined on capacity spaces, instead of measure spaces. It is our feeling that these developments, because of their relations with important aspects of mathematical analysis on one hand and their simple and basic character on the other, deserve to be widely known.

over the unit square MSC (2010) Primary: 46B70; Secondary: 46E30Dedicated to Professor Hans Triebel on the occasion of his 75th birthday.We study limit K-spaces for general Banach couples, not necessarily ordered. They correspond to the extreme choice θ = 0, 1 in the realization of the real method as a K-space. We also show the connection of these limit spaces with interpolation methods defined by the unit square.

We investigate limiting J-interpolation methods for general Banach couples, not necessarily ordered. We also show their relationship with the interpolation methods defined by the unit square.

No abstract

No abstract