Peetre's inequality

The Peetre 's inequality, named after Jaak Peetre, is an inequality from the mathematical branch of functional analysis, specifically from the theory of Hilbert spaces.

It is a Hilbert space. Then for all and for all real numbers, the inequality

This inequality was proved in 1959 by J. Peetre and is used for numerical and theoretical estimates. If one above inequality to

Order, it can be seen that this estimate may be helpful in Sobolev spaces of real-valued order, because there occur under one integral on just functions of the form. An application of the Peetre 's inequality in this direction can be found in the below textbook in the study of multiplication operators on Sobolev spaces.