Interpolation of Cesàro sequence and function spaces

• Autorzy: Sergey V. Astashkin , Lech Maligranda
• Języki publikacji: EN

Abstrakty

EN

The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that $Ces_{p}(I)$ is an interpolation space between $Ces_{p₀}(I)$ and $Ces_{p₁}(I)$ for 1 < p₀ < p₁ ≤ ∞ and 1/p = (1 - θ)/p₀ + θ/p₁ with 0 < θ < 1, where I = [0,∞) or [0,1]. The same result is true for Cesàro sequence spaces. On the other hand, $Ces_{p}[0,1]$ is not an interpolation space between Ces₁[0,1] and $Ces_{∞}[0,1]$.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 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: 2013
• Tom: 215
• Numer: 1
• Strony: 39-69

Daty

wydano

2013

Twórcy

autor

Sergey V. Astashkin

• Department of Mathematics and Mechanics, Samara State University, Acad. Pavlova 1, 443011 Samara, Russia

autor

Lech Maligranda

• Department of Engineering Sciences and Mathematics, Luleå University of Technology, SE-971 87 Luleå, Sweden

Identyfikatory

DOI

10.4064/sm215-1-4