A priori estimates for higher order multipliers on a circle

Authors:
A. Alexandrou Himonas and Gerard Misiolek

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 | References | Similar Articles | Additional Information

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

Email:
alex.a.himonas.1@nd.edu

**Gerard Misiolek**

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

DOI:
https://doi.org/10.1090/S0002-9939-02-06439-0

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