Young's convolution inequality

Imagine you have two shapes, A and B. A can be any shape you can think of, like a square or a circle. B is just a little line, but it can be any length.

Now, pretend you are going to move shape B around on shape A. You can slide it around, just like sliding your pencil along a piece of paper. When you slide it around, you can think of it as multiplying the values of A and B at each point. This gives you a new shape, called a convolution.

Young's convolution inequality is just a fancy way of saying that when you add up all the values in the convolution shape, it will always be less than or equal to the product of the highest value in shape A and the length of shape B.

Let's say that the highest value of A is 5, and the length of B is 3. When you slide B around on A, you get a new shape where the highest value is 15. Young's convolution inequality tells you that adding up all the values in this new shape will always be less than or equal to 15 times 3, which is 45.

So, in short, Young's convolution inequality is a way of making sure that when you slide one shape around on another shape to make a new shape, the values in the new shape don't get too big. It's like making sure you don't use too much paint when painting on a canvas.