On the Restriction of The Fourier Transform to Curves: Endpoint Results and The Degenerate Case
On the Restriction of The Fourier Transform to Curves: Endpoint Results and The Degenerate Case
For smooth curves $\Gamma$ in ${{\mathbf {R}}^n}$ with certain curvature properties it is shown that the composition of the Fourier transform in ${{\mathbf {R}}^n}$ followed by restriction to $\Gamma$ defines a bounded operator from ${L^p}({{\mathbf {R}}^n})$ to ${L^q}(\Gamma )$ for certain $p,q$. The curvature hypotheses are the weakest under which …