Fourier Restriction Implies Maximal and Variational Fourier Restriction in Lorentz Space

In this paper, we show that Fourier restriction theorem implies the maximal and variational Fourier restriction in Lorentz space frame. The key ingredient is that we work out the induction argument in Lorentz space, based on some good properties of Lorentz space. This extends Kovač's result J. Funct. Anal., 2019, 277(10): 3355–3372 to Lorentz space frame.