Research Article

Spectrum of the Cesàro-Hardy operator in rearrangement invariant spaces

Published in: Quaestiones Mathematicae
Volume 47 , issue 6 , 2024 , pages: 1157–1175

DOI: 10.2989/16073606.2023.2281570

Author(s): Meiram Akhymbek Institute of Mathematics and Mathematical Modeling, Kazakhstan , Kanat Tulenov Institute of Mathematics and Mathematical Modeling, Kazakhstan , Gulnur Zaur Institute of Mathematics and Mathematical Modeling, Kazakhstan

Keywords: 47A10 , 47A75 , 46E30 , Rearrangement invariant spaces , Lorentz L_p , q spaces , Cesàro-Hardy operator , spectrum , fine spectra

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Abstract

In this paper, we investigate the spectrum of the Cesàro-Hardy operator in rearrangement invariant spaces over a finite interval and a half line, thereby extending Boyd’s and Leibowitz’s results for Lp(1 < p ⩽ 8) spaces. In particular, when our rearrangement invariant space is the Lorentz space L_p,q , a full description of the spectrum and fine spectra is presented.

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