子流形上平均的秩与正则性
Rank and regularity for averages over submanifolds
摘要：
本文建立了满足齐性条件（类似于半拟齐性）和与旋转曲率有关的矩阵秩条件的Radon-like算子的端点$L^p-L^q$和Sobolev映射性质.对于高度退化的运营商，秩条件一般满足代数的原因，类似于观察Greenleaf，Pramanik，唐关于振荡积分运营商。
英文摘要：
This paper establishes endpoint $L^p-L^q$ and Sobolev mapping properties of Radon-like operators which satisfy a homogeneity condition (similar to semiquasihomogeneity) and a condition on the rank of a matrix related to rotational curvature. For highly degenerate operators, the rank condition is generically satisfied for algebraic reasons, similar to an observation of Greenleaf, Pramanik, and Tang concerning oscillatory integral operators.
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