Due to its lower density, warmer air is under lower pressure than cooler air.
Explanation
Air pressure is due to the density of the air.
The air density depends on the space between the molecules.
If the molecules are closely packed, then the air is said to be dense and vice-versa.
In the atmosphere, air which is at the bottom has more density than air at the top.
Therefore, air at the bottom has a higher density than air at the top.
Another factor like temperature also plays a vital role in air pressure.
In higher temperature, air becomes warm, air molecules become free and density lowers.