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Multilinear extrapolation and applications to the bilinear Hilbert transform |
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| Authors: | María Jesús Carro Loukas Grafakos José María Martell Fernando Soria |
| Institution: | a Departament de Matemàtica Aplicada i Anàlisi, Universitat de Barcelona, E-08071 Barcelona, Spain b Department of Mathematics, University of Missouri, Columbia, MO 65211, USA c Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, Consejo Superior de Investigaciones Científicas, C/ Serrano 121, E-28006 Madrid, Spain d Departamento de Matemáticas, C-XV, Universidad Autónoma de Madrid, E-28049 Madrid, Spain |
| Abstract: | We present two extrapolation methods for multi-sublinear operators that allow us to derive estimates for general functions from the corresponding estimates on characteristic functions. Of these methods, the first is applicable to general multi-sublinear operators while the second requires working with the so-called (ε,δ)-atomic operators. Among the applications, we discuss some new endpoint estimates for the bilinear Hilbert transform. |
| Keywords: | Multilinear extrapolation Restricted weak type estimates _method=retrieve& _eid=1-s2 0-S0022247X09003138& _mathId=si2 gif& _pii=S0022247X09003138& _issn=0022247X& _acct=C000051805& _version=1& _userid=1154080& md5=0ce25ba657ec2028ec78361518199462')" style="cursor:pointer (ε" target="_blank">" alt="Click to view the MathML source" title="Click to view the MathML source">(ε δ)-atomic operators Galb Bilinear Hilbert transform |
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