Coefficient Condition for L -Convergence of 1 Walsh]Fourier Series

In this paper we give a condition with respect to Walsh]Fourier coefficients that implies the L1-convergence of the corresponding Walsh]Fourier series. We show that the L1-convergence class induced by this condition contains each one of the previously known convergence classes as a proper subset. We also show that our condition implies not only the L1-convergence but also the convergence in the dyadic Hardy norm if the function represented by the series belongs to the dyadic Hardy space.