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arXiv · 2006.07008

Besov spaces associated with non-negative operators on Banach spaces

Charles Batty·Chuang Chen
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Abstract

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.

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Charles Batty, Chuang Chen. 2020-06-12. Besov spaces associated with non-negative operators on Banach spaces. https://arxiv.org/abs/2006.07008

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