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Zeitschrift für Analysis und ihre Anwendungen


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Volume 32, Issue 2, 2013, pp. 233–255
DOI: 10.4171/ZAA/1483

Published online: 2013-04-08

Hardy Averaging Operator on Generalized Banach Function Spaces and Duality

Yoshihiro Mizuta[1], Aleš Nekvinda[2] and Tetsu Shimomura[3]

(1) Hiroshima Institute of Technology, Japan
(2) Czech Technical University, Praha, Czech Republic
(3) Hiroshima University, Graduate School of Education, Higashi-Hiroshima, Japan

Let $Af(x):=\frac{1}{|B(0,|x|)|} \int_{B(0,|x|)} f(t) \ dt$ be the $n$-dimensional Hardy averaging operator. It is well known that $A$ is bounded on $L\sp p(\Omega)$ with an open set $\Omega \subset \R^n$ whenever $1

Keywords: Hardy averaging operator, Lebesgue spaces of variable exponent, Banach function space, optimal domain

Mizuta Yoshihiro, Nekvinda Aleš, Shimomura Tetsu: Hardy Averaging Operator on Generalized Banach Function Spaces and Duality. Z. Anal. Anwend. 32 (2013), 233-255. doi: 10.4171/ZAA/1483