On a counterexample related to weighted weak type estimates for singular\n integrals

2015/06/27 by Marcela Caldarelli, Andrei K. Lerner, Caldarelli, Marcela +3
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems

paper · pdf · doi:10.48550/arxiv.1506.08317

Abstract

We show that the Hilbert transform does not map L¹(M_\Φw) to\nL^1,\∞(w) for every Young function \Φ growing more slowly than\nt\log\log ( rm e ^{rm e}+t). Our proof is based on a construction of M.C.\nReguera and C. Thiele.\n

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