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The Hardy spaces for Fourier integral operators for
Naijia Liu, Jan Rozendaal, Liang Song
We introduce the Hardy spaces for Fourier integral operators for , thereby extending earlier constructions for .…
and regularity for wave equations with rough coefficients
Naijia Liu, Jan Rozendaal, Liang Song
We consider second-order hyperbolic equations with rough time-independent coefficients. Our main result is that such equations are well posed on the Hardy spaces $\mathcal{H}^{s,1}…
Global solutions to 3D quadratic nonlinear Schrödinger-type equation
Zihua Guo, Naijia Liu, Liang Song
We consider the Cauchy problem to the 3D fractional Schrödinger equation with quadratic interaction of type. We prove the global existence of solutions and scattering pro…
Lp bounds for Stein's spherical maximal operators
Naijia Liu, Minxing Shen, Liang Song +1
Let be the spherical maximal operators of complex order on . In this article we show that when , suppose \begin{eqnarray*} \|{\frak M}^α f…
Local smoothing and Hardy spaces for Fourier integral operators on manifolds
Naijia Liu, Jan Rozendaal, Liang Song +1
We introduce the Hardy spaces for Fourier integral operators on Riemannian manifolds with bounded geometry. We then use these spaces to obtain improved local smoothing estimates fo…