I have been studying this preprinted paper and the references there in. I believe that there are some typos; However, since I am not an expert yet, so I would like to make sure I am correct.

1. I think that there must be missing $\| g\|_{L^2}^2$ in the fourth inequality in the proof of theorem 2.5.
2. I do not understand how the author made the restriction in the paragraph after equation (2.5)? in particular $ l \le 2j+2$.
3. Why he fixed $\Lambda = 2^{2j+5}$

Thanks in Advance.

I have been studying this preprinted paper and the references therein. I believe that there are some typos; However, since I am not an expert yet, I would like to make sure I am correct.

I do not understand how the author made the restriction in the paragraph after equation (2.5)? in particular $ l \le 2j+2$.

Thanks in Advance.