相关论文: Interpolator symmetries and new Kalton-Peck spaces
The so-called Kalton-Peck space $Z_2$ is a twisted Hilbert space induced, using complex interpolation, by $c_0$ or $\ell_p$ for any $1\leq p\neq 2<\infty$. Kalton and Peck developed a scheme of results for $Z_2$ showing that it is a very…
The Kalton-Peck $Z_2$ space is the derived space obtained from the scale of $\ell_p$ spaces by complex interpolation at $1/2$. If we denote by by $Z_2^{real}$ the derived space obtained from the scale of $\ell_p$ spaces by real…
Kalton and Mitrea characterized complex interpolation spaces of quasi-Banach function spaces as Calder\'on products if both interpolants are separable. We show that one separability assumption may be omitted and establish a…
We present a formula for the interpolation of matrix weighted spaces of vector valued functions via interpolation functors. We apply our formula to the particular case of interpolation of matrix weighted $L^p$ spaces by the real and complex…
In this paper, we introduce the so-called elliptic Askey-Wilson polynomials which are homogeneous polynomials in two special theta functions. With regard to the significance of polynomials of such kind, we establish some general elliptic…
We study complex interpolation of weighted Besov and Lizorkin-Triebel spaces. The used weights $w_0,w_1$ are local Muckenhoupt weights in the sense of Rychkov. As a first step we calculate the Calder\'on products of associated sequence…
This is the second of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. One of the many…
We extend our work on nonseparated interpolating sequences, originally developed for Bergman spaces with weights of the form $(1 - |z|^2)^\alpha$, to more general weights.
This paper contains no new results. It is intended to be merely a brief introduction to the long paper: N. J. Kalton, Differentials of complex interpolation processes for Kothe function spaces. Trans. Amer. Math. Soc. 333 (1992), no. 2,…
Known or essentially known results about duals of interpolation spaces are presented, taking a point of view sometimes slightly different from the usual one. Particular emphasis is placed on Alberto Calderon's theorem describing the duals…
The complex method of interpolation, going back to Calder\'on and Coifman et al., on the one hand, and the Alexander-Wermer-Slodkowski theorem on polynomial hulls with convex fibers, on the other hand, are generalized to a method of…
We characterize interpolating sequences for pairs of reproducing kernels $(s, \ell)$, where $s$ is a complete Pick factor of $\ell.$ This answers a question of Aleman, Hartz, McCarthy and Richter.
We prove the stability of isomorphisms between Banach spaces generated by interpolation methods introduced by Cwikel-Kalton-Milman-Rochberg which includes, as special cases, the real and complex methods up to equivalence of norms and also…
This is the third of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It does not contain new results. This time, rather…
We show that Rochberg's generalizared interpolation spaces $\mathscr Z^{(n)}$ arising from analytic families of Banach spaces form exact sequences $0\to \mathscr Z^{(n)} \to \mathscr Z^{(n+k)} \to \mathscr Z^{(k)} \to 0$. We study some…
Given a metric measure space $X$, we consider a scale of function spaces $T^{p,q}_s(X)$, called the weighted tent space scale. This is an extension of the tent space scale of Coifman, Meyer, and Stein. Under various geometric assumptions on…
The Rademacher series in rearrangement invariant function spaces "closed" to the space L_\infty are considered. In terms of interpolation theory of operators a correspondence between such spaces and spaces of coefficients generated by them…
We consider interpolation inequalities for imbeddings of the $l^2$-sequence spaces over $d$-dimensional lattices into the $l^\infty_0$ spaces written as interpolation inequality between the $l^2$-norm of a sequence and its difference. A…
In this paper, we first introduce some new kinds of weighted amalgam spaces. Then we discuss the strong type and weak type estimates for a class of Calder\'on--Zygmund type operators $T_\theta$ in these new weighted spaces. Furthermore, the…
This is the fourth of a series of papers surveying some small part of the remarkable work of our friend and colleague Nigel Kalton. We have written it as part of a tribute to his memory. It contains almost no new results. This time we…