A generalization of two classical convergence tests for Fourier series, and some new Banach spaces of functions

B. Korenblum
1983 Bulletin of the American Mathematical Society  
The norms of these spaces fill the gap between the uniform and the variation norms. Their duals are described in terms of generalized variation. One application of these spaces is a new convergence test for Fourier series which includes both the Dirichlet-Jordan and the Dini-Lipschitz tests [1],
doi:10.1090/s0273-0979-1983-15160-1 fatcat:3r7tlb4qgzdv3lnxlmgfn4qpxe