Estimates for maximal functions associated to hypersurfaces in ℝ³ with height h < 2: Part I

Simple item page
dc.contributor.authorBuschenhenke, Stefan
dc.contributor.authorDendrinos, Spyridon
dc.contributor.authorIkromov, Isroil A.
dc.contributor.authorMüller, Detlef
dc.contributor.funderDeutsche Forschungsgemeinschaften
dc.contributor.funderNational Science Foundationen
dc.contributor.funderMathematical Sciences Research Institute, Berkeley, Californiaen
dc.date.accessioned2019-08-30T10:22:35Z
dc.date.available2019-08-30T10:22:35Z
dc.date.issued2019-07-15
dc.date.updated2019-08-30T09:58:06Z
dc.description.abstractIn this article, we continue the study of the problem of Lp-boundedness of the maximal operator M associated to averages along isotropic dilates of a given, smooth hypersurface S of finite type in 3-dimensional Euclidean space. An essentially complete answer to this problem was given about eight years ago by the third and fourth authors in joint work with M. Kempe [Acta Math 204 (2010), pp. 151–271] for the case where the height h of the given surface is at least two. In the present article, we turn to the case h < 2. More precisely, in this Part I, we study the case where h < 2, assuming that S is contained in a sufficiently small neighborhood of a given point x0 ∈ S at which both principal curvatures of S vanish. Under these assumptions and a natural transversality assumption, we show that, as in the case h ≥ 2, the critical Lebesgue exponent for the boundedness of M remains to be pc = h, even though the proof of this result turns out to require new methods, some of which are inspired by the more recent work by the third and fourth authors on Fourier restriction to S. Results on the case where h < 2 and exactly one principal curvature of S does not vanish at x0 will appear elsewhere.en
dc.description.sponsorshipDeutsche Forschungsgemeinschaft (DFG-Grant MU 761/11-1); National Science Foundation (Grant No. DMS-1440140)en
dc.description.statusPeer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationBuschenhenke, S., Dendrinos, S., Ikromov, I. A. and Müller, D. (2019) 'Estimates for maximal functions associated to hypersurfaces in ℝ³ with height h < 2: Part I', Transactions of the American Mathematical Society, 372(2), pp. 1363-1406. doi: 10.1090/tran/7633en
dc.identifier.doi10.1090/tran/7633en
dc.identifier.eissn1088-6850
dc.identifier.endpage1406en
dc.identifier.issn0002-9947
dc.identifier.issued2en
dc.identifier.journaltitleTransactions of the American Mathematical Societyen
dc.identifier.startpage1363en
dc.identifier.urihttps://hdl.handle.net/10468/8418
dc.identifier.volume372en
dc.language.isoenen
dc.publisherAmerican Mathematical Societyen
dc.rights© 2019, American Mathematical Society. First published in Transactions of the American Mathematical Society 372(2), July 2019. This author's draft version of the work, after peer review, is reproduced under the CC BY-NC-ND Creative Commons License.en
dc.rights.urihttps://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectSmooth hypersurfaceen
dc.subject3-dimensional Euclidean spaceen
dc.subjectIsotropic dilatesen
dc.titleEstimates for maximal functions associated to hypersurfaces in ℝ³ with height h < 2: Part Ien
dc.typeArticle (peer-reviewed)en
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
hless2-rev5_(002).pdf
Size:
429.63 KB
Format:
Adobe Portable Document Format
Description:
Accepted Version
Download
License bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
2.71 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Collections
Mathematical Sciences- Journal Articles