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A Unified Geometric Perspective on Zygmund's Maximal Function Conjecture and Related Questions for the Stein Hilbert Transform
The Zygmund vector-field maximal function conjecture is a long-standing open problem in harmonic analysis. It is notoriously difficult in part because the vector-field maximal function is non-translation-invariant and lies beyond the scope of finite-type theory. Its resolution would yield a Lebesgue
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