# Sharp Wirtinger's type inequalities for double integrals with Applications

## TL;DR

This paper establishes sharp Wirtinger-type inequalities for double integrals and applies them to derive new sharp byev inequalities for absolutely continuous functions with second derivatives in L^2.

## Contribution

It introduces novel sharp inequalities for double integrals and extends these results to byev inequalities for functions with specific smoothness.

## Key findings

- Derived sharp Wirtinger inequalities for double integrals.
- Proved new sharp byev inequalities for functions with second derivatives in L^2.
- Extended classical inequalities using these new bounds.

## Abstract

In this work, sharp Wirtinger type inequalities for double integrals are established. As applications, two sharp \v{C}eby\v{s}ev type inequalities for absolutely continuous functions whose second partial derivatives belong to $L^2$ space are proved.