You need to add mulch to the bottom of the tree so the ground will not dry out so fast. You need to stay on top of a regular wattering schedule. Water is the single most important thing to Japanese maples. The tree may be getting too much sun. It should see sun in our zone 'till about 11:00AM or noon and shade for the rest of the day.

Anytime you plant a new tree, you have to keep the soil moist for at least the first season. Not wet. There needs to be room for oxygen so the roots can take it in for photosynthesis. You can afford to neglect it A LITTLE after that first season. By this time the roots should be out finding water. LA is humid right? So, watch how much water you put down. Since it is humid, it will not lose water through the leaves as fast as it would in a dry or windy climate. In a humid area, you could easily over water a tree and kill it. The symptom is the same as underwatering it. Wilting. Just papmer it. Stick your finger in the soil. Make sure its not dry. Yeah, mulch will assist you keeping the soil from drying out. But, if you use mulch remember that mulch will absorb a lot of water itself.

So, your leaves turned brown? This is a sign of death. But, don't lose hope. The tree may still be alive. Very gently bend the branches and trunk and listen. If it is flexable without a cracking sound, there is moisture in there. That is a good sign. It may have just gone dormant to save its life. But, usually this early dormancy will look like a fall color show. Brown is not one of them. If it is dormant, you should have another chance next season. Stop watering it now.

If it is dry there are cuts you can make at the base of the tree that will stimulate growth. I have to be honest with you, I don't know much about that. If I remember right, you can make a cut through the bark just above the soil line. Put mulch over it several inches and water it in the spring. But, this could introduce disease into the tree from the mulch.