Boundedness of Functions on Product Spaces by Sums of Functions on the Factors

TL;DR

This paper explores conditions under which functions on product spaces can be bounded by sums or products of functions defined on individual factors, aiding understanding of their boundedness properties.

Contribution

It provides new sufficient conditions for bounding functions on product spaces using functions on individual factors, advancing the theoretical framework.

Findings

Established criteria for bounding functions on product spaces

Connected boundedness conditions to factor-dependent functions

Enhanced understanding of function behavior on complex spaces

Abstract

We investigate sufficient conditions for real-valued functions on product spaces to be bounded from above by sums or products of functions which depend only on points in the respective factors.