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.
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fractional leibniz Leibniz formula |
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fractional lebniz fomular leibniz formula |
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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. |
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