A precomposition analysis of linear operators on $l^ p$
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- by Steve M. Hudson PDF
- Proc. Amer. Math. Soc. 111 (1991), 227-233 Request permission
Abstract:
Given a function $g$, the operator that sends the function $f(x)$ to the function $f(g(x))$ is called a precomposition operator. If $g$ preserves measure on its domain, at least approximately, then this operator is bounded on all the ${L^p}$ spaces. We ask which operators can be written as an average of precomposition operators. We give sufficient, almost necessary conditions for such a representation when the domain is a finite set. The class of operators studied approximate many commonly used positive operators defined on ${L^p}$ of the real line, such as maximal operators. A major tool is the combinatorial theorem of distinct representatives, commonly called the marriage theorem. A strong connection between this theorem and operators of weak-type 1 is demonstrated.References
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Additional Information
- © Copyright 1991 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 111 (1991), 227-233
- MSC: Primary 47B37; Secondary 47B38
- DOI: https://doi.org/10.1090/S0002-9939-1991-1031666-8
- MathSciNet review: 1031666