Estimates for the norm of the hardy operator in operator ideals

E. N. Lomakina, M. G. Nasyrova

Computer Centre of Far Eastern Branch RAS, Khabarovsk

Abstract: We find the conditions for a compact Hardy operator in Lorentz spaces to belong to the operator ideals generated by sequences of $s$-numbers. We obtain some estimates of the norms of the Hardy operator in these ideals in terms of integral expressions depending on the weight functions of the operator.

Keywords: operator ideal, Hardy operator, Lorentz spaces, approximation numbers, $s$-numbers.

UDC: 517.98

MSC: 35R30

Received: 16.08.2023
Revised: 25.10.2023
Accepted: 28.11.2023

DOI: 10.33048/smzh.2024.65.208

 English version: Siberian Mathematical Journal, 2024, 65:2, 328–343