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

Tom 170 / 2005

Irina Asekritova, Natan Krugljak, Ludmila Nikolova 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

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