2023/02/02 by Ikeda, Masahiro, Ishikawa, Isao, Taniguchi, Koichi
#30H25 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 47B33 #Secondary 46E35
paper · doi:10.48550/arxiv.2302.00811
This paper aims to characterize boundedness of composition operators on Besov spaces Bsp,q of higher order derivatives s>1+1/p on the one-dimensional Euclidean space. In contrast to the lower order case 01. We prove a relation between the composition operators and pointwise multipliers of Besov spaces, and effectively use the characterizations of the pointwise multipliers. As a result, we obtain necessary and sufficient conditions for the boundedness of composition operators for general p, q, and s such that 11+1/p. In this paper, we treat, as a map that induces the composition operator, not only a homeomorphism on the real line but also a continuous map whose number of elements of inverse images at any one point is bounded above. We also show a similar characterization of the boundedness of composition operators on Sobolev spaces.