Convergence of multiple Vilenkin–Fourier series in Lorentz spaces

Let $\Lambda_{\psi,p}[0,1)^d$ be a near to $L^\infty[0,1)^d$ Lorentz space. We find the function $\tilde\psi$ for which the multiple Vilenkin–Fourier of any $f\in\Lambda_{\psi,p}[0,1)^d$ converge to $f$ in the norm of Lorentz space $\Lambda_{\bar\psi,p}[0,1)^d$.