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