Fourier restriction to curves and related operators

Author / Creator

Jesurum, Michael, author

Available as

Online

Physical

Summary

This thesis focuses on Fourier restriction operators, both classical and maximal, associated with curves. In the classical case, we prove new Lp to Lq inequalities for restriction to curves with fe...

This thesis focuses on Fourier restriction operators, both classical and maximal, associated with curves. In the classical case, we prove new Lp to Lq inequalities for restriction to curves with few derivatives, using the affine arclength measure and powers thereof. In particular, we prove Fourier restriction inequalities in the optimal range for smooth curves in dimensions d [greater than or equal to] 3. We also apply these techniques to two other well-studied operators: convolution with measures along curves and a family of restricted X-ray transforms. In the maximal case, we consider the moment curve in dimensions d [greater than or equal to] 3 and via direct methods, we prove new inequalities.

Show More