M.D.
You've got to get very firm. Hitting should NOT be tolerated, especially hitting mom! I know he's young, but he's not too young to learn that. He must never be rewarded for hitting - for example, he hits to get your attention so you can't give him your attention - move him away or walk away, he hits to get a toy, so he cannot have that toy.
It's hard to use a time-out and expect a one yr old to stay there, but you can VERY sternly in an angry voice say "No hitting" or "No, hitting Mommy!" and then move him away - across the room to a chair perhaps. Or even put him in the next room... he won't stay there but he will get that you are not tolerating it and that it results in just the opposite of what he wants.
Some, may disagree, but this is not the time to talk sweetly and nicely... "Oh, honey, we don't hit, do we? No, hitting is ouchy, hands are not for hitting!" It won't work. He's one and he learns more by your tone of voice, not what you are saying. With my first, I called it the big, mean voice and it really got her attention because I hardly ever used it. Not yelling, just very stern and louder than normal. Just that voice was consequence enough to make her stop - she was hitting to get my attention or get what she wanted and that mean voice is definitely not what she wanted.
Good luck. It's a normal stage for little ones, but get tough now so he learns that hitting is not okay and does not get him what he wants. :)