论文标题
在加权伯格曼空间上，汉克尔形式的两种重量不平等。
Two weight inequality for Hankel form on weighted Bergman spaces induced by doubling weights
论文作者
论文摘要
小型汉克尔操作员$ h_f^ν（g）=p_ν（f \ bar {g}）$，由分析符号$ f $和伯格曼预测$p_ν$与$ $ν$相关的伯格曼投影$p_ν$，由加权bergman space $ a^p_ p_ p_ p_ p_ p_ p_ p_ p_ p_ p_ p _^q_ $ a^q_ p y Inf the Of the Om a^Q_ $ω，ν$属于radial权重的类$ \ MATHCAL {D} $，承认某些双面双面条件。获得的某些结果等效于双线性汉克尔形式的界限，这些形式又用于建立弱分解$a_η^{q} =a_Ω^{p_ {p_ {1}} \ odota_ν^^{p_ {p_ {p_ {2}}} $，其中$ 1 <q，wer $ q^{ - 1} = p_ {1}^{ - 1}+p_ {2}^{ - 1} $ and $ \widetildeη^{\ frac {1} {q}} \ asymp \ asymp \wideTildeΩ^{\ frac {1} {p_ {1}}}} \wideTildeCν^{\ frac {\ frac {\ frac {1} {1} {p_ {2} {2}}}} $。这里$ \widetildeτ（r）= \ int_r^1τ（t）\，dt/（1-t）$ for ahl $ 0 \ le l r <1 $。
The boundedness of the small Hankel operator $h_f^ν(g)=P_ν(f\bar{g})$, induced by an analytic symbol $f$ and the Bergman projection $P_ν$ associated to $ν$, acting from the weighted Bergman space $A^p_\om$ to $A^q_ν$ is characterized on the full range $0<p,q<\infty$ when $ω,ν$ belong to the class $\mathcal{D}$ of radial weights admitting certain two-sided doubling conditions. Certain results obtained are equivalent to the boundedness of bilinear Hankel forms, which are in turn used to establish the weak factorization $A_η^{q}=A_ω^{p_{1}}\odot A_ν^{p_{2}}$, where $1<q,p_{1},p_{2}<\infty$ such that $q^{-1}=p_{1}^{-1}+p_{2}^{-1}$ and $\widetildeη^{\frac{1}{q}}\asymp\widetildeω^{\frac{1}{p_{1}}}\widetildeν^{\frac{1}{p_{2}}}$. Here $\widetildeτ(r)=\int_r^1τ(t)\,dt/(1-t)$ for all $0\le r<1$.
