$Estimates for maximal functions associated to hypersurfaces in $\Bbb R^3$ with height $h<2:$ Part II -- A geometric conjecture and its proof for generic 2-surfaces$

Estimates for maximal functions associated to hypersurfaces in $\Bbb R^3$ with height $h<2:$ Part II -- A geometric conjecture and its proof for generic 2-surfaces

In this article, we continue the study of $L^p$-boundedness of the maximal operator $\mathcal M_S$ associated to averages along isotropic dilates of a given, smooth hypersurface $S$ in 3-dimensional Euclidean space. We focus here on small surface-patches near a given point $x^0$ exhibiting s...

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Veröffentlicht in:	arXiv.org 2022-09
Hauptverfasser:	Buschenhenke, Stefan, Ikromov, Isroil A, Müller, Detlef
Format:	Artikel
Sprache:	eng
Schlagworte:	Ellipsoids Euclidean geometry Euclidean space Hyperspaces Mathematical analysis Operators (mathematics)
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Estimates for maximal functions associated to hypersurfaces in \(\Bbb R^3\) with height \(h<2:\) Part II -- A geometric conjecture and its proof for generic 2-surfaces