JournalsrmiVol. 19, No. 1pp. 221–234

Mapping properties of the elliptic maximal function

  • M. Burak Erdoğan

    University of Illinois, Urbana, United States
Mapping properties of the elliptic maximal function cover

Abstract

We prove that the elliptic maximal function maps the Sobolev space W4,η(R2)W_{4,\eta}(\mathbb{R}^2) into L4(R2)L^4(\mathbb{R}^2) for all η>1/6\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.

Cite this article

M. Burak Erdoğan, Mapping properties of the elliptic maximal function. Rev. Mat. Iberoam. 19 (2003), no. 1, pp. 221–234

DOI 10.4171/RMI/344