Spectrum of the Cesàro-Hardy operator in rearrangement invariant spaces

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.

Mathematics Subject Classification (2020):

• 47A10
• 47A75
• 46E30

Key words:

• Rearrangement invariant spaces
• Lorentz L_p,q spaces
• Cesàro-Hardy operator
• spectrum
• fine spectra