1. Boundedness of composition operators on higher order Besov spaces in one dimension.
- Author
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Ikeda, Masahiro, Ishikawa, Isao, and Taniguchi, Koichi
- Abstract
This paper aims to characterize boundedness of composition operators on Besov spaces B p , q s of higher order derivatives s > 1 + 1 / p on the one-dimensional Euclidean space. In contrast to the lower order case 0 < s < 1 , there were a few results on the boundedness of composition operators for s > 1 . 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 1 < p ≤ ∞ , 0 < q ≤ ∞ , and s > 1 + 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. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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