The operator (1+L_A)^{-γ/2} e^{it√L_A} is bounded on Lp(R^2) for all 1<p<∞ whenever γ>|1/p-1/2|, with norm growing like (1+t)^γ.
Papageorgiou, Oscillating multipliers on rank one lo cally symmetric spaces, Journal of Mathematical Analysis and Applications, 494 (2021)
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$L^p$-estimates for the 2D wave equation in the scaling-critical magnetic field
The operator (1+L_A)^{-γ/2} e^{it√L_A} is bounded on Lp(R^2) for all 1<p<∞ whenever γ>|1/p-1/2|, with norm growing like (1+t)^γ.