# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

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

### Tom 170 / 2005

Studia Mathematica 170 (2005), 227-239 MSC: Primary 46B70; Secondary 46E30. DOI: 10.4064/sm170-3-2

#### Streszczenie

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.

#### Autorzy

• Irina AsekritovaMatematiska och Systemtekniska Institutionen
Växjö University
351 95 Växjö, Sweden
e-mail
• Natan KrugljakDepartment of Mathematics
Luleå University of Technology
SE 972 33 Luleå, Sweden
e-mail
• Ludmila NikolovaUniversity of Sofia
boul. James Boucher 5
Sofia 1164, Bulgaria
e-mail

## Przeszukaj wydawnictwa IMPAN

Zbyt krótkie zapytanie. Wpisz co najmniej 4 znaki.

Odśwież obrazek