Remark on the Strichartz estimates in the radial case (Q655490)

The purpose of the paper is to prove Strichartz estimates for fractional powers of the Laplacian and radial initial data microlocalized at frequency \( 2^k \) (with \(k \in {\mathbb Z} \)). The result is that if \( u (t) = \exp (it|D|^a) u_0 \) then \[ \| u \|_{L^q_t L^r_x} \leq C 2^{k \big( \frac{n}{2} - \frac{a}{q} - \frac{n}{r} \big)} \| u_0 \|_{L^2}, \] provided that \(u_0\) is radially symmetric, that its Fourier transform is localized near \( |\xi| \sim 2^k \) and \[ n \geq 2, \qquad a > 0, \;a \neq 1, \quad 2 \leq q \leq \infty, \quad \frac{2}{q} + \frac{2n-1}{r} \leq n - \frac{1}{2}, \qquad (q,r) \neq \Big( 2 , \frac{4n-2}{2n-3} \Big). \]