The Fourier-Walsh series of the functions absolutely continuous in the generalized restricted sense.

We consider the questions of convergence in Lorentz spaces for the Fourier-Walsh series of the functions with Denjoy integrable derivative. We prove that a condition on a function f sufficient for its Fourier-Walsh series to converge in the Lorentz spaces “near” L ∞ cannot be expressed in terms of the growth of the derivative f′. [ABSTRACT FROM AUTHOR]