Mapping properties of the elliptic maximal function.
M. Burak Erdogan (2003)
Revista Matemática Iberoamericana
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We prove that the elliptic maximal function maps the Sobolev space W4,eta(R2) into L4(R2) for all eta > 1/6. The main ingredients of the proof are an analysis of the intersectiQn properties of elliptic annuli and a combinatorial method of Kolasa and Wolff.