Riesz potential

Have you ever wondered how objects and people are attracted to each other? For example, have you noticed that objects on a slanted plane slide downwards because of gravity? Well, Riesz potential is like gravity but it's not just for physical objects, it is for functions!

Functions are like tools that mathematicians use to study and solve problems. With Riesz potential, we study how functions attract or repel each other. Just like gravity has a pull on objects, Riesz potential has a pull on functions.

Let's imagine you have a friend who is walking towards you. You can feel his presence, right? Now imagine you have a basket full of balls and you drop one ball into the basket. The ball attracts other balls towards it, and they all get stuck together. Similarly, with Riesz potential, the function pulls other functions towards it.

But wait, there's more! Just like gravity has an inverse square law, which means that the force between two objects decreases with the square of the distance between them, Riesz potential also has an inverse power law. This means that the strength of the pull between two functions decreases as the distance between them increases.

So, to sum it up, Riesz potential is like gravity but for functions. It studies how functions attract or repel each other, just like how physical objects are attracted to each other by gravity. It has an inverse power law, which means that the strength of the pull decreases with the distance between them.