No cite, nor am I am expert on such things, but I am thinking that the skin on your palms and soles isn’t any different than the stuff on the rest of your body. It just happens that your palms and soles are the parts of your body that are the least frequently exposed to sunlight. Your hands are usually grabbing things, holding things, making fists, or most of the rest of the time just loafing about half curled, palms facing the body. About the only time your palms ever get exposed directly to the sunlight is when they’re extended and face up as you wait for someone to hand you something. Your feet? Well, they spent most of their time on the ground. The rest of the time they’re more or less perpendicular to the sun – say, when you’re lounging around with your feet up. Unless you’ve made it a habit to sunbathe with your legs hoisted high, they don’t get much sun either – although when you’re lying on your back, the soles of your feet do get aimed in a more upward direction, so it’s possible that they could get a bit more exposure in the normal course of deliberate sunbathing.
The skin on the soles of most people’s feet is more delicate though – at least in the arch, where it seldom makes contact with anything besides socks. Because of that, the nerve endings are closer to the surface due to there being less callous material covering them. They also see the least amount of sunlight, what with usually being covered by footwear. That would make them more likely to burn than tan, but I see no reason that they couldn’t be affected by the sun the same way the rest of your skin is, given an equal opportunity to do so.