论文标题
与Banach空间上的非负操作员相关的空间
Besov spaces associated with non-negative operators on Banach spaces
论文作者
论文摘要
由运算符的分数能力的各种表示的动机，我们开发了抽象的理论space spaces $ b^{s，a} _ {q，x} $，用于非阴性运算符$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ x $，带有全范围的indices $ s \ in \ in \ inthbb {r} $ {r} $ 0 <q \ 0 <q \ sftty。我们使用的方法是针对非阴性操作员的分解的二元分解，这是对古典BESOV空间构建中Littlewood-Paley分解的类似物。特别是，通过对BESOV空间的运算符和明确的准标准估算的复制公式，我们讨论了与操作员相关的BESOV空间的平稳性与基础操作员分数幂的界限之间的连接。
Motivated by a variety of representations of fractional powers of operators, we develop the theory of abstract Besov spaces $B^{ s, A }_{ q, X }$ for non-negative operators $A$ on Banach spaces $X$ with a full range of indices $s \in \mathbb{R}$ and $0 < q \leq \infty$. The approach we use is the dyadic decomposition of resolvents for non-negative operators, an analogue of the Littlewood-Paley decomposition in the construction of the classical Besov spaces. In particular, by using the reproducing formulas for fractional powers of operators and explicit quasi-norms estimates for Besov spaces we discuss the connections between the smoothness of Besov spaces associated with operators and the boundedness of fractional powers of the underlying operators.
