论文标题
外部$ l^p_μ（\ ell^r）$空间和与帐篷空间的关系
Duality for outer $L^p_μ(\ell^r)$ spaces and relation to tent spaces
论文作者
论文摘要
我们证明，由do and thiele引入的外部$ l^p_μ（\ ell^r）$空间对Banach空间是同构的，我们在它们之间以$ 1 <p \ leq \ infty，1 \ leq leq r <\ infty $或$ p = r \ in \ in \ in \ in \ instruity in \ int \ int \ int \ ins \ ins \ int \ ins \ int \ ins \ int \ ins \ ins \ int \ int \ int \ ins \ int \ int \ int \ int \ ins \ infty in。在$ p = 1，1 <r \ leq \ infty $的情况下，我们将展示一个均匀性的反例。我们表明，在上半部空间中，设置这些属性在整个范围内$ 1 \ leq p，r \ leq \ infty $。这些结果是通过$ l^p_μ（\ ell^r）$的贪婪分解来获得的。结果，我们在上半部空间中建立了经典帐篷空间$ t^p_r $与外部$ l^p_μ（\ ell^r）$空间之间的等价性。最后，我们对在$ \ mathbb {r}^d $上的函数的分数尺度因子进行嵌入到上半部分的嵌入地图的弱和强类型估计的完整分类。
We prove that the outer $L^p_μ(\ell^r)$ spaces, introduced by Do and Thiele, are isomorphic to Banach spaces, and we show the expected duality properties between them for $1 < p \leq \infty, 1 \leq r < \infty$ or $p=r \in \{ 1, \infty \}$ uniformly in the finite setting. In the case $p=1, 1 < r \leq \infty$, we exhibit a counterexample to uniformity. We show that in the upper half space setting these properties hold true in the full range $1 \leq p,r \leq \infty$. These results are obtained via greedy decompositions of functions in $L^p_μ(\ell^r)$. As a consequence, we establish the equivalence between the classical tent spaces $T^p_r$ and the outer $L^p_μ(\ell^r)$ spaces in the upper half space. Finally, we give a full classification of weak and strong type estimates for a class of embedding maps to the upper half space with a fractional scale factor for functions on $\mathbb{R}^d$.
