Remarks on some dispersive estimates
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.
scientific article; zbMATH DE number 5989652