On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded

Abstract

Abstract We show that the necessity part of the main result of [L. Diening, O. Karlovych and E. Shargorodsky, On interpolation of reflexive variable Lebesgue spaces on which the Hardy–Littlewood maximal operator is bounded, Georgian Math. J. 29 2022, 3, 347–352] can be derived easily from its predecessor [2, Theorem 4.1] and its sufficiency part.