A precomposition analysis of linear operators on

Author:
Steve M. Hudson

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

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Abstract: Given a function , the operator that sends the function to the function is called a precomposition operator. If preserves measure on its domain, at least approximately, then this operator is bounded on all the 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 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.

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DOI:
https://doi.org/10.1090/S0002-9939-1991-1031666-8

Article copyright:
© Copyright 1991
American Mathematical Society