Entropy Numbers of Embeddings of Weighted Besov Spaces
Entropy Numbers of Embeddings of Weighted Besov Spaces
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DOI：
10.1007/s00365-005-0594-9
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发表时间：
2005-06
影响因子：
2.7
通讯作者：
Thomas Kuhn;Hans-Gerd Leopold;W. Sickel;L. Skrzypczak
中科院分区：
文献类型：
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作者：
Thomas Kuhn;Hans-Gerd Leopold;W. Sickel;L. Skrzypczak
我们研究了紧嵌入B^{S_1}_{p_1，q_1}(\mbox{足注大小\bf R}^d，\α)\钩右目标B^{S_2}_{p_2，q_2}({xxR})的熵数的渐近行为。$$这里$B^S_{p，q}\！({\Mbox{\Footnote Size\bf R}^d}，\α)$表示加权Besov空间，其中权重由给出，$B^{S_2}_{p_2，q_2}\！({\Mbox{\Footnote Size\bf R}^d})$表示未加权Besov空间。我们将集中讨论由下列参数星座给出的所谓的极限情形：，和$$\α=S_1-\FRAC{d}{p_1}-S_2+\FRAC{d}{p_2}>；d\，\max\Big(0，\FRAC{1}{p_2}-\FRAC{1}{p_1}\BIG)。在几乎所有的情况下，我们都会给出一个精确的两边估计。
We investigate the asymptotic behavior of the entropy numbers of the compact embedding $$ B^{s_1}_{p_1,q_1} \!\!(\mbox{\footnotesize\bf R}^d, \alpha) \hookrightarrow B^{s_2}_{p_2,q_2} \!\!({\xxR}). $$ Here $B^s_{p,q} \!({\mbox{\footnotesize\bf R}^d}, \alpha)$ denotes a weighted Besov space, where the weight is given by, and $B^{s_2}_{p_2,q_2} \!({\mbox{\footnotesize\bf R}^d})$ denotes the unweighted Besov space, respectively. We shall concentrate on the so-called limiting situation given by the following constellation of parameters:,, and $$ \alpha = s_1 - \frac{d}{p_1} - s_2 + \frac{d}{p_2} > d \, \max \Big(0, \frac{1}{p_2}-\frac{1}{p_1}\Big). $$ In almost all cases we give a sharp two-sided estimate.