The Lizorkin–Freitag formula for several weighted $L_{p}$ spaces and vector-valued interpolation

Irina Asekritova¹ ; Natan Krugljak² ; Ludmila Nikolova³

¹ Matematiska och Systemtekniska Institutionen Växjö University 351 95 Växjö, Sweden
² Department of Mathematics Luleå University of Technology SE 972 33 Luleå, Sweden
³ University of Sofia boul. James Boucher 5 Sofia 1164, Bulgaria

Studia Mathematica, Tome 170 (2005) no. 3, pp. 227-239

Résumé

A complete description of the real interpolation space $$ L=(L_{p_{0}}(\omega _{0}),\ldots,L_{p_{n}}(\omega _{n}))_{\vec{\theta},q} $$ is given. An interesting feature of the result is that the whole measure space $({\mit\Omega},\mu )$ can be divided into disjoint pieces ${\mit\Omega} _{i}$ ($i\in I$) such that $L$ is an $l_{q}$ sum of the restrictions of $L$ to ${\mit\Omega} _{i}$, and $L$ on each ${\mit\Omega} _{i}$ is a result of interpolation of just two weighted $L_{p}$ spaces. The proof is based on a generalization of some recent results of the first two authors concerning real interpolation of vector-valued spaces.

Détail

DOI : 10.4064/sm170-3-2

Keywords: complete description real interpolation space omega ldots omega vec theta given interesting feature result whole measure space mit omega divided disjoint pieces mit omega nbsp sum restrictions mit omega each mit omega result interpolation just weighted spaces proof based generalization recent results first authors concerning real interpolation vector valued spaces