We construct an example showing that the upper bound [w]A1 log(e+[w]A1) for the L1(w) → L1,∞(w) norm of the Hilbert transform cannot be improved in general.
Bibliographical noteFunding Information:
Lerner is supported by ISF grant No. 447/16 and ERC Starting Grant No. 713927, Nazarov is supported by U.S. National Science Foundation grant DMS-1600239, Ombrosi is supported by CONICET PIP 11220130100329CO, Argentina. MSC2010: 42B20, 42B25. Keywords: Hilbert transform, maximal operator, weighted inequalities.
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- Hilbert transform
- Maximal operator
- Weighted inequalities