4 edited body; edited title

# fractional leibnizLeibniz formula

Let $T=(-\triangle)^{\frac{1}{2}}$,Can we have similar estimates below hold in $L^p$ ? $\| T^{\alpha}(fg)-(T^{\alpha}f)g-f(T^{\alpha}g) \|_p \leq \|T^{\alpha-1}f\|_p \|T^{\alpha-1}g\|_p$, where $\alpha>0$,p>1. If we really have such fractional lebniz fomular Leibniz formula holds,we can then estimate the fractional intergration integration by parts also.

3 edited title; edited title

# fractional lebnizfomularleibnizformula

2 deleted 11 characters in body; deleted 2 characters in body; added 13 characters in body; added 2 characters in body; deleted 10 characters in body

Let $T=(-\triangle)^{\frac{1}{2}}$,Can we have similar estimates below hold in $L^p$ ? $\| T^{\alpha}(fg)-(T^{\alpha}f)g-f(T^{\alpha}g) \|_p \leq \|T^{\alpha-1}f\|_p \|T^{\alpha-1}g\|_p$, where $10$ \alpha>0\$,p>1. If we really have such fractional lebniz fomular holds,we can then estimate the fractional intergration by parts also.

1