Abstract
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.
Original language | English |
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Pages (from-to) | 1939-1954 |
Number of pages | 16 |
Journal | Analysis and PDE |
Volume | 13 |
Issue number | 6 |
DOIs | |
State | Published - 2020 |
Bibliographical note
Publisher Copyright:© 2020 Mathematical Sciences Publishers.
Funding
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.
Funders | Funder number |
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U.S. National Science Foundation | DMS-1600239 |
Horizon 2020 Framework Programme | 713927 |
European Commission | |
Consejo Nacional de Investigaciones Científicas y Técnicas | PIP 11220130100329CO, MSC2010 |
Israel Science Foundation | 447/16 |
Keywords
- Hilbert transform
- Maximal operator
- Weighted inequalities