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arXiv · 1702.03988

On $L^p$-improving for averages associated to mixed homogeneous polynomial hypersurfaces in $\mathbb{R}^3$

Spyridon Dendrinos·Eugen Zimmermann
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Abstract

We establish $L^p-L^q$ estimates for averaging operators associated to mixed homogeneous polynomial hypersurfaces in $\mathbb{R}^3$. These are described in terms of the mixed homogeneity and the order of vanishing of the polynomial hypersurface and its Gaussian curvature transversally to their zero sets.

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Spyridon Dendrinos, Eugen Zimmermann. 2017-02-13. On $L^p$-improving for averages associated to mixed homogeneous polynomial hypersurfaces in $\mathbb{R}^3$. https://arxiv.org/abs/1702.03988

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