Mapping properties of the elliptic maximal function

M. Burak Erdoǧan

doi:10.4171/RMI/344

Mapping properties of the elliptic maximal function

Research output: Contribution to journal › Article › peer-review

Abstract

We prove that the elliptic maximal function maps the Sobolev space W_4,η(ℝ²) into L⁴(ℝ²) for all η > 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.

Original language	English (US)
Pages (from-to)	221-234
Number of pages	14
Journal	Revista Matematica Iberoamericana
Volume	19
Issue number	1
DOIs	https://doi.org/10.4171/RMI/344
State	Published - 2003
Externally published	Yes

Keywords

Circular maximal function
Multiparameter maximal functions
Sobolev space estimates

ASJC Scopus subject areas

Mathematics(all)

Online availability

10.4171/RMI/344

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KW - Multiparameter maximal functions

KW - Sobolev space estimates

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Mapping properties of the elliptic maximal function

Abstract

Keywords

ASJC Scopus subject areas

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