We characterise those real analytic mappings between any pair of tori which carry absolutely convergent Fourier series to uniformly convergent Fourier series via composition. We do this with respect to rectangular summation. We also investigate uniform convergence with respect to square sums and highlight the differences which arise.
The Hermite-Hadamard inequality in higher dimensions
On a theorem of M. Cartwright in higher dimensions
Carleson's $\varepsilon^2$ conjecture in higher dimensions
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