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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 ,doi:10.1090/s0273-0979-1983-15160-1 fatcat:3r7tlb4qgzdv3lnxlmgfn4qpxe