Carleman's inequality

Carleman's inequality is a mathematical result in the field of functional analysis and approximation theory. It provides a bound on the norms of a function based on the norms of its derivatives. Specifically, it is often used in the context of the spaces of functions with certain smoothness properties. One of the most common forms of Carleman's inequality is related to the Sobolev spaces and is used to show the equivalence of certain norms.