# Markov's inequality on Koornwinder's domain in $L^p$ norms

## TL;DR

This paper establishes the optimal exponent in Markov's inequality for a specific domain in the plane within $L^p$ norms, advancing understanding of polynomial inequalities on complex domains.

## Contribution

It determines the exact exponent value (4) for Markov's inequality on Koornwinder's domain in $L^p$ norms, which was previously unknown.

## Key findings

- Optimal exponent in Markov's inequality is 4.
- The result applies to the domain defined by $ ext{Omega}$ in the plane.
- Provides a precise mathematical characterization of polynomial bounds.

## Abstract

Let $\Omega=\{(x,y) \in \mathbb{R}^2 : |x|<y+1, \, x^2>4y\}$. We prove that the optimal exponent in Markov's inequality on $\Omega$ in $L^p$ norms is 4.