Lorentz-Shimogaki-Arazy-Cwikel Theorem Revisited

Abstract

We present a new approach to Lorentz-Shimogaki and Arazy-Cwikel Theorems which covers all range of $p,q\in (0,\infty ]$ for function spaces and sequence spaces. As a byproduct, we solve a conjecture of Levitina and the last two authors.

27 pages

References in corpus (3)

• Cwikel estimates revisited
• Interpolation between $L_0(\mathcal{M},\tau )$ and $L_{\infty }(\mathcal{M},\tau )$
• Arazy-Cwikel and Calderón-Mityagin type properties of the couples $({\ell }^p,{\ell }^q)$, $0\le p<q\le \infty$