Coefficient condition for L-1-convergence of Walsh-Fourier series

[摘要] In this paper we give a condition with respect to Walsh-Fourier coefficients that implies the L(1)-convergence of the corresponding Walsh-Fourier series. We show that the L(1)-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 L(1)-convergence but also the convergence in the dyadic Hardy norm if the function represented by the series belongs to the dyadic Hardy space. (C) 1997 Academic Press.

[发布日期] 1997-06-15