Interpolation of Cesàro sequence and function spaces

Sergey V. Astashkin, and Lech Maligranda. "Interpolation of Cesàro sequence and function spaces." Studia Mathematica 215.1 (2013): 39-69. <http://eudml.org/doc/285675>.

@article{SergeyV2013,
abstract = {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 $Ces_\{∞\}[0,1]$.},
author = {Sergey V. Astashkin, Lech Maligranda},
journal = {Studia Mathematica},
keywords = {Cesàro sequence and function spaces; weighted Cesàro function spaces; copson sequence and function spaces; interpolation; K-functional; K-method of interpolation},
language = {eng},
number = {1},
pages = {39-69},
title = {Interpolation of Cesàro sequence and function spaces},
url = {http://eudml.org/doc/285675},
volume = {215},
year = {2013},
}

TY - JOUR
AU - Sergey V. Astashkin
AU - Lech Maligranda
TI - Interpolation of Cesàro sequence and function spaces
JO - Studia Mathematica
PY - 2013
VL - 215
IS - 1
SP - 39
EP - 69
AB - 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 $Ces_{∞}[0,1]$.
LA - eng
KW - Cesàro sequence and function spaces; weighted Cesàro function spaces; copson sequence and function spaces; interpolation; K-functional; K-method of interpolation
UR - http://eudml.org/doc/285675
ER -