Endpoint $L^p \to L^q$ bounds for integration along certain polynomial curves
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.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2017
- DOI:
- arXiv:
- arXiv:1710.07668
- Bibcode:
- 2017arXiv171007668S
- Keywords:
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- Mathematics - Classical Analysis and ODEs
- E-Print:
- This is a preprint version of a published article. The final version is in J. Funct. Anal. 259 (2010), no. 12, 3205-3229