Interpolation of Cesàro sequence and function spaces

Tom 215 / 2013

Sergey V. Astashkin, Lech Maligranda Studia Mathematica 215 (2013), 39-69 MSC: Primary 46E30, 46B70; Secondary 46B20. DOI: 10.4064/sm215-1-4

Streszczenie

The interpolation properties of Cesàro sequence and function spaces are investigated. It is shown that ${\rm Ces}_p(I)$ is an interpolation space between ${\rm Ces}_{p_0}(I)$ and ${\rm Ces}_{p_1}(I)$ for $1 < p_0 < p_1 \leq \infty $ and $1/p = (1 - \theta )/p_0 + \theta /p_1$ with $0 < \theta < 1$, where $I = [0, \infty )$ or $[0, 1]$. The same result is true for Cesàro sequence spaces. On the other hand, ${\rm Ces}_p[0, 1]$ is not an interpolation space between ${\rm Ces}_1[0, 1]$ and ${\rm Ces}_{\infty }[0, 1]$.

Autorzy

  • Sergey V. AstashkinDepartment of Mathematics and Mechanics
    Samara State University
    Acad. Pavlova 1
    443011 Samara, Russia
    e-mail
  • Lech MaligrandaDepartment of Engineering Sciences
    and Mathematics
    Luleå University of Technology
    SE-971 87 Luleå, Sweden
    e-mail

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