Multipliers of Fourier–Haar series in Lorentz spaces

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].