The Schrödinger equation in $L^{p}$ spaces for operators with heat kernel satisfying Poisson type bounds

On complex-time heat kernels of fractional Schrödinger operators via Phragmén–Lindelöf principle

“…Complex-time heat kernel estimates like (1.2) are of paramount importance in many problems in harmonic analysis and partial differential equations, e.g., in proving L p boundedness of spectral multipliers and convergence of Riesz means, and investigating maximal regularity properties of the Schrödinger evolution e it H for operators H whose heat kernels satisfy sub-Gaussian estimates, see, e.g., [5][6][7][8][9][10]14,15,[17][18][19][20][21]27,28,37,47,59].…”