Smooth and singular maximal averages over 2D hypersurfaces and associated Radon transforms
نویسندگان
چکیده
We prove Lp boundedness results, p>2, for local maximal averaging operators over a smooth 2D hypersurface S with either C1 density function or singularity that grows as |(x,y)|−β β<2. Suppose one is in coordinates such the surface localized near some (x0,y0,z0) at which (0,0,1) normal to surface, and suppose represented graph of z0+s(x−x0,y−y0) (x0,y0), s(0,0)=0. It shown long Taylor series Hessian determinant s(x,y) (0,0) not identically zero, operator bounded on p>max(2,1/g), where g an index based growth rate distribution origin. Standard examples show exponent 1/g best possible whenever tangent plane does contain This theorem improves main result [19], using different methods. use closely related methods Lαp Sobolev estimates Radon transform same functions, no excluded cases. In g<1/2 case, there interval I containing 2 proven α<g when p∈I, p can never gain more than derivatives.
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ژورنال
عنوان ژورنال: Advances in Mathematics
سال: 2021
ISSN: ['1857-8365', '1857-8438']
DOI: https://doi.org/10.1016/j.aim.2020.107465