Endpoint $L^p \to L^q$ bounds for integration along certain polynomial curves

Betsy Stovall

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arXiv · 1710.07668

Endpoint $L^p \to L^q$ bounds for integration along certain polynomial curves

Betsy Stovall

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Abstract

We establish strong-type endpoint $L^p(\mathbb R^d) \to L^q(\mathbb R^d)$ bounds for the operator given by convolution with affine arclength measure on polynomial curves for $d \geq 4$. The bounds established depend only on the dimension $d$ and the degree of the polynomial.

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Betsy Stovall. 2017-10-20. Endpoint $L^p \to L^q$ bounds for integration along certain polynomial curves. https://arxiv.org/abs/1710.07668

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