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March, 2003 Mapping properties of the elliptic maximal function
Mehmet Burak Erdoğan
Rev. Mat. Iberoamericana 19(1): 221-234 (March, 2003).


We prove that the elliptic maximal function maps the Sobolev space $W_{4,\eta}(\mathbb{R}^2)$ into $L^4(\mathbb{R}^2)$ for all $\eta>1/6$. The main ingredients of the proof are an analysis of the intersection properties of elliptic annuli and a combinatorial method of Kolasa and Wolff.


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Mehmet Burak Erdoğan. "Mapping properties of the elliptic maximal function." Rev. Mat. Iberoamericana 19 (1) 221 - 234, March, 2003.


Published: March, 2003
First available in Project Euclid: 31 March 2003

zbMATH: 1037.42024
MathSciNet: MR1993421

Primary: 42B25

Keywords: circular maximal function , Multiparameter maximal functions , Sobolev space estimates

Rights: Copyright © 2003 Departamento de Matemáticas, Universidad Autónoma de Madrid

Vol.19 • No. 1 • March, 2003
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