FORWARD AND REVERSE CARLESON INEQUALITIES FOR FUNCTIONS IN BERGMAN SPACES AND THEIR DERIVATIVES
FORWARD AND REVERSE CARLESON INEQUALITIES FOR FUNCTIONS IN BERGMAN SPACES AND THEIR DERIVATIVES
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DOI：
10.2307/2374458
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发表时间：
1985-02
影响因子：
1.7
通讯作者：
D. Luecking
中科院分区：
文献类型：
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作者：
D. Luecking
是满意的。在此过程中，得到了HP中函数导数上的一些不等式的一个简单证明（第3节），以及关于LP的插值序列的一些信息（第5节）。像（1.1）这样的不等式已经被用来提供关于Bergman-Toeplitz算子的信息[L1]，并且对于在Lp中获得函数的表示很有用（第4节，定理4.6）。（1.1）中颠倒了A和m的作用的不等式相对容易——即使在m中包含了适当的权重因子（下面的定理A）。它是由Oleinik和Pavlov [OP]和Stegenga [S]和Hastings [Ha]独立得出的（当p = q > 1时）。Oleinik和Pavlov的结果（比定理A更普遍）在[0]中得到了Oleinik的推广。Cima和Wogen [CW]利用Stegenga的方法证明了定理A在几个变量上的类似性。[L3]的方法或多或少地取代了所有这些结果。
is satisfied. In the process, a simple proof of certain inequalities on derivatives of functions in HP is obtained (Section 3) as well as some information on interpolation sequences for LP (Section 5). Inequalities like (1.1) have already been used to provide information on Bergman-Toeplitz operators [L1] and are useful for obtaining representations of functions in Lp (Section 4, Theorem 4.6). The inequality which reverses the roles of A and m in (1.1) is relatively easy-even if an appropriate weighting factor is included with m (Theorem A below). It was obtained by Oleinik and Pavlov [OP] and independently (when p = q > 1) by Stegenga [S] and (with c = 0) Hastings [Ha]. The results of Oleinik and Pavlov (which are more general than Theorem A) were extended somewhat by Oleinik in [0]. Cima and Wogen [CW], using Stegenga's methods, proved the analogue of Theorem A in several variables. The methods of [L3] more or less supercede all these results.