Some new Fourier inequalities for unbounded orthogonal systems in Lorentz-Zygmund spaces

Abstract

In this paper we prove some essential complements of the paper (J. Inequal. Appl. 2019:171, 2019) on the same theme. We prove some new Fourier inequalities in the case of the Lorentz–Zygmund function spaces L q,r (logL ) α Lq,r(log⁡L)α involved and in the case with an unbounded orthonormal system. More exactly, in this paper we prove and discuss some new Fourier inequalities of this type for the limit case L 2,r (logL ) α L2,r(log⁡L)α , which could not be proved with the techniques used in the paper