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A priori estimates for higher order multipliers on a circle


Authors: A. Alexandrou Himonas and Gerard Misiołek
Journal: Proc. Amer. Math. Soc. 130 (2002), 3043-3050
MSC (1991): Primary 42B15; Secondary 35G25
DOI: https://doi.org/10.1090/S0002-9939-02-06439-0
Published electronically: March 14, 2002
MathSciNet review: 1908929
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Abstract: We present an elementary proof of an a priori estimate of Bourgain for a general class of multipliers on a circle using an extension of methods developed in our previous work. The main tool is a suitable version of a counting argument of Zygmund for unbounded regions.


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Additional Information

A. Alexandrou Himonas
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
MR Author ID: 86060
Email: alex.a.himonas.1@nd.edu

Gerard Misiołek
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556 – and – Isaac Newton Institute for Mathematical Sciences, University of Cambridge, Cambridge, CB3 9EW, United Kingdom
Email: misiolek.1@nd.edu

Keywords: Fourier transform, multiplier inequalities, interpolation
Received by editor(s): May 29, 2001
Published electronically: March 14, 2002
Additional Notes: Both authors were partially supported by the NSF under grant number DMS-9970857 and by the Faculty Research Program of the University of Notre Dame.
The second author was also supported by the Isaac Newton Institute for Mathematical Sciences of the University of Cambridge.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2002 American Mathematical Society