2020/06/12 by C. J. K. Batty, Chuang Chen, Batty, Charles +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Physics Problems #Differential Equations and Boundary Problems
paper · pdf · doi:10.48550/arxiv.2006.07008
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 ∈ ℝ and 0 < q ≤ ∞. 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.