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

• Autorzy: Irina Asekritova , Natan Krugljak , Ludmila Nikolova
• Języki publikacji: EN

Abstrakty

EN

A complete description of the real interpolation space
$L = (L_{p₀}(ω₀),...,L_{pₙ}(ωₙ))_{θ⃗,q}$
is given. An interesting feature of the result is that the whole measure space (Ω,μ) can be divided into disjoint pieces $Ω_{i}$ (i ∈ I) such that L is an $l_{q}$ sum of the restrictions of L to $Ω_{i}$, and L on each $Ω_{i}$ 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.

Kategorie tematyczne

• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 46B70: Interpolation between normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2005
• Tom: 170
• Numer: 3
• Strony: 227-239

Daty

wydano

2005

Twórcy

autor

Irina Asekritova

• Matematiska och Systemtekniska Institutionen, Växjö University, 351 95 Växjö, Sweden

autor

Natan Krugljak

• Department of Mathematics, Luleå University of Technology, SE 972 33 Luleå, Sweden

autor

Ludmila Nikolova

• University of Sofia, boul. James Boucher 5, Sofia 1164, Bulgaria

Identyfikatory

DOI

10.4064/sm170-3-2