Remarks on some dispersive estimates (Q652023)

The authors derive dispersive estimates of the solution to the initial value problem to the general dispersive equation \[ i\partial_t u+\omega(|\nabla|)u=0 \;\text{ in } \mathbb R^{n+1}, \quad u(0)=\varphi \;\text{ in } \mathbb R^n, \] under suitable smoothness and growth conditions on \(\omega.\) They unify and simplify all the known dispersive estimates by utilizing the Bessel function and extend them to more general cases.