We obtain the following two inequalities on a strongly pseudoconvex domain $Omega$ in ${mathbb C}^n$ : for $finmathcal O(Omega)$ egin{align*} int_0^{delta_0} t^{a|lpha|+b} M_p^a (t, D^lpha f) ,dt &lesssimint_0^{delta_0} t^{b} M_p^a (t, f) ,dt int_0^{delta_0} t^{b} M_p^a (t, f),dt &lesssim sum_{j=0}^mint_0^{delta_0} t^{am+b} M_p^aBig(t,mathcal N^j fBig) ,dt. end{align*} In cite{S}, Shi proved these results for the unit ball in ${Bbb C}^n$. These are generalizations of some classical results of Hardy and Littlewood.
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机译:我们在$ { mathbb C} ^ n $中的强伪凸域$ Omega $上获得以下两个不等式:对于$ f in mathcal O( Omega)$ begin {align *} int_0 ^ { delta_0} t ^ {a | alpha | + b} M_p ^ a(t,D ^ alpha f),dt& lesssim int_0 ^ { delta_0} t ^ {b} M_p ^ a(t,f ),dt int_0 ^ { delta_0} t ^ {b} M_p ^ a(t,f),dt& lesssim sum_ {j = 0} ^ m int_0 ^ { delta_0} t ^ {am + b} M_p ^ a Big(t, mathcal N ^ jf Big),dt。 end {align *}在 cite {S}中,Shi用$ { Bbb C} ^ n $证明了单位球的这些结果。这些是Hardy和Littlewood的一些经典结果的概括。
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