Revista Matemática Iberoamericana


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Volume 19, Issue 1, 2003, pp. 221–234
DOI: 10.4171/RMI/344

Published online: 2003-04-30

Mapping properties of the elliptic maximal function

M. Burak Erdoğan[1]

(1) University of Illinois, Urbana, United States

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.

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

Erdoğan M. Burak: Mapping properties of the elliptic maximal function. Rev. Mat. Iberoamericana 19 (2003), 221-234. doi: 10.4171/RMI/344