Decay and Strichartz estimates in critical electromagnetic fields

Maximal estimates for fractional Schrödinger equations in scaling critical magnetic fields

“…which includes the usual wave and Schrödinger equation as two special cases. The dispersive and Strichartz estimates associated with the magnetic Schrödinger operator L A have been extensively studied in [11,13,16] and we also refer to [12,15] for the resolvent estimates.…”

“…Very recently, Fanelli-Zhang-Zheng [12] used the spectral measure constructed in [16] to prove the following resolvent estimates.…”

“…where for the definition of d s and B α (s, θ 1 , θ 2 ) we can refer to [16]. From [16, (1.25)], one has |d s | 2 ≥ (r 1 + r 2 ) 2 ≥ |x − y| 2 .…”

Dispersive estimates for two-particles Schrödinger and wave equations in the Aharonov-Bohm field

“…In this paper, we continue our program [6,15,18] studying the dispersive equations in Aharonov-Bohm field. The Aharonov-Bohm magnetic potential reads…”

“…In R 2 , a generalization of H A was considered in [11,12] in which the dispersive estimates were proved for Schrödinger equation. Recently, in [15,18], the authors have proved the Strichartz estimates for wave and Klein-Gordon equations in the Aharonov-Bohm magnetic fields. It worths mentioning that the wave and Klein-Gordon equations are lack of pseudoconformal invariance which plays an important role in [11] for Schrödinger equation, hence we have to use a new method in [15,18].…”