论文标题
混合序列和基质空间中存在几乎贪婪的基础，包括besov空间
Existence of almost greedy bases in mixed-norm sequence and matrix spaces, including Besov spaces
论文作者
论文摘要
我们证明了序列$ \ ell_p \ oplus \ ell_q $和无限矩阵的空间besov空间，只要$ 0 <p <q <q <\ infty $，都会有几乎贪婪的基础。更确切地说，我们定制了几乎贪婪的基础，以使Lebesgue参数以规定的方式生长。我们的论点在很大程度上取决于[S. S. J. Dilworth，N。J。Kalton和D. Kutzarova，关于Banach空间中几乎贪婪的基础，Studia Math。 159（2003），否。 1，67-101]最初设计用于在Banach空间中构造几乎贪婪的基础，以使其对于具有非局部凸组件的混合式空间的直接总和有效。此外，我们证明，这些空间的所有几乎所有贪婪基地的基本功能随着$（m^{1/q}）_ {m = 1}^\ infty $而生长。
We prove that the sequence spaces $\ell_p\oplus\ell_q$ and the spaces of infinite matrices $\ell_p(\ell_q)$, $\ell_q(\ell_p)$ and $(\bigoplus_{n=1}^\infty \ell_p^n)_{\ell_q}$, which are isomorphic to certain Besov spaces, have an almost greedy basis whenever $0<p<1<q<\infty$. More precisely, we custom-build almost greedy bases in such a way that the Lebesgue parameters grow in a prescribed manner. Our arguments critically depend on the extension of the Dilworth-Kalton-Kutzarova method from [S. J. Dilworth, N. J. Kalton, and D. Kutzarova, On the existence of almost greedy bases in Banach spaces, Studia Math. 159 (2003), no. 1, 67-101], which was originally designed for constructing almost greedy bases in Banach spaces, to make it valid for direct sums of mixed-normed spaces with nonlocally convex components. Additionally, we prove that the fundamental functions of all almost greedy bases of these spaces grow as $(m^{1/q})_{m=1}^\infty$.
