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In this note we complete a circle of results presented in §5 of an earlier work of the author (J. Fourier Anal. 5 (1999), 449-463), establishing the endpoint case of Proposition 10 of that paper. As a consequence, we have results on pointwise convergence of the Fourier series (summed by spheres) of a function on the 3-dimensional torus with a simple jump across a smooth surface Σ, with no curvature hypotheses on Σ, extending Proposition 7 of that paper.doi:10.1090/s0002-9939-00-05789-0 fatcat:de67hfyjmvaa3itxt7u7uscoty