Multipliers of Fourier-Haar Series in Lorentz Spaces

Abstract

This article provides a complete description of the multipliers of the Fourier series along the Haar system in the Lorentz spaces \(L_{p,r}\). Necessary and sufficient conditions are obtained ensuring that \(\{\lambda_k^j\}_{k=0,j=1}^{\infty,2^k} \in m(L_{p,r} \to L_{q,s})\). This work generalizes and supplements the result of work [8].