Yup... pretty common place.

Try to relax your hands a little, and not grip the bars too tight.
As you get used to downhills you'll find you sit on the brakes less and that will help too.

The thing is, you are asking your hands to do something new, and until they get used to it, like any other muscles they are gonna feel sore, tired and worked-over.

Give it time and it should get better.