# A note on Hardy-type inequalities in variable exponent Lebesgue spaces

## TL;DR

This paper establishes new estimates for Hardy-type inequalities within variable exponent Lebesgue spaces, demonstrating that under certain regularity conditions, these estimates can be simplified to fixed exponent cases.

## Contribution

The paper introduces a novel approach to reduce Hardy-type inequality estimates in variable exponent spaces to fixed exponent scenarios under regularity assumptions.

## Key findings

- New estimates for Hardy-type inequalities in variable exponent Lebesgue spaces.
- Reduction of variable exponent estimates to fixed exponent cases.
- Conditions under which the reduction is valid.

## Abstract

We present new estimate for Hardy-type inequality in variable exponent Lebesgue spaces. More precisely, by imposing regularity assumptions on the exponent, we prove that the estimations can be reduced to the fixed exponents.