Complex interpolation of variable Triebel–Lizorkin spaces

Interpolation in Variable Exponent Spaces

In this paper we study both real and complex interpolation in the recently introduced scales of variable exponent Besov and Triebel–Lizorkin spaces. We also take advantage of some interpolation results to study a trace property and some pseudodifferential operators acting in the variable index Besov scale.

Interpolation Spaces by Complex Methods

where the infimum is taken over all pairs x^ÇzXj satisfying (2.1). One easily checks that (2.2) gives a norm on X 0 + X i when X0 and X% are compatible. Moreover, when X0+Xi is equipped with this norm, it becomes a Banach space (cf. [3]). Let Cfc denote the set of complex valued functions of the complex variable f = ̂ +irf which are continuous on bounded subsets of S, where fl is the strip 0 <£ ...

Complex interpolation of weighted noncommutative Lp-spaces

Let M be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace τ . Let d be an injective positive measurable operator with respect to (M, τ ) such that d is also measurable. Define Lp(d) = {x ∈ L0(M) : dx+ xd ∈ Lp(M)} and ‖x‖Lp(d) = ‖dx+ xd‖p . We show that for 1 6 p0 < p1 6 ∞, 0 < θ < 1 and α0 > 0, α1 > 0 the interpolation equality (Lp0(d 0), Lp1(d α))θ = Lp(d ) hol...

Complex Interpolation and Twisted Twisted Hilbert Spaces

Differentials of Complex Interpolation Processes for Kothe Function Spaces

We continue the study of centralizers on Kothe function spaces and the commutator estimates they generate (see [29]). Our main result is that if X is a super-reflexive Kothe function space then for every real centralizer Q on X there is a complex interpolation scale of Kothe function spaces through X inducing Q as a derivative, up to equivalence and a scalar multiple. Thus, in a loose sense, al...