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The $L\log L$ Fourier-convergence conjecture

Proves that the ordinary symmetric Fourier partial sums of every complex-valued function in

L\log L(\mathbb T)

converge almost everywhere along the full sequence. This resolves the classical sufficiency conjecture at the

L\log L

scale.

Manuscripts in this family · 1

Sep 23, 2026·paper.pdfLean

We prove that the ordinary symmetric Fourier partial sums of every complex-valued function in

L\log L

on the circle converge almost everywhere to the function along the full sequence. This establishes the classical

L\log L

sufficiency conjecture.

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