boundedness of maximal averages over hypersurfaces in

Author:
Michael Greenblatt

Journal:
Trans. Amer. Math. Soc. **365** (2013), 1875-1900

MSC (2010):
Primary 42B20

Published electronically:
September 19, 2012

MathSciNet review:
3009647

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Abstract: Extending the methods developed in the author's recent paper and using some techniques from a paper by Sogge and Stein in conjunction with various facts about adapted coordinate systems in two variables, an boundedness theorem is proven for maximal operators over hypersurfaces in when When the best possible is greater than , the theorem typically provides sharp estimates. This gives another approach to the subject of recent work of Ikromov, Kempe, and Müller (2010).

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Additional Information

**Michael Greenblatt**

Affiliation:
Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 322 Science and Engineering Offices, 851 S. Morgan Street, Chicago, Illinois 60607-7045

DOI:
https://doi.org/10.1090/S0002-9947-2012-05697-2

Received by editor(s):
April 27, 2011

Published electronically:
September 19, 2012

Additional Notes:
This research was supported in part by NSF grant DMS-0919713

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.