During the assault on pearl harbor, Japan was clearly in the advantageous position to claim a piece of U.S. territory, what I'm confused on is to why they decided to retreat and fall back, wouldn't have been better to go with the momentum and attempt an assault upon California??
I talk about this here.
First, the Japanese fleet wasn't outfitted for an amphibious assault of Hawaii. The Pearl Harbor attack was supposed to be a decisive blow to prevent the US from entering the war, not an occupying force. Second, Japan didn't have the resources to sustain an occupation. If I remember correctly, the fleet that attacked Pearl Harbor used up a not-insignificant portion of Japan's oil reserves just traveling to and from Hawaii. The IJN simply couldn't run a 2,500 mile supply line to Hawaii. That's also why the Japanese military couldn't use Hawaii as a staging ground for a mainland invasion: the distance between Hawaii and the continental United States is almost as large as the distance between New York and Los Angeles.
Would also recommend this article from Combined Fleet, a website run by the authors of the best current book on midway, which also examines this issue, Shattered Sword: http://www.combinedfleet.com/pearlops.htm
Frankly put nobody in Japan seriously thought they could pull it off, and nobody thought it would be worthwhile to try and supply that large of a number of bodies. The islands in 1941 were not self sufficient and feeding the garrison and population of just Oahu, even on starvation rations would have been difficult in the extreme for the comparatively tiny merchant marine of Japan.
There simply were not the number of ships around to even get the 60k or so troops it was thought it might take(which given the terrain of Oahu severely favored the defenders who would outnumber the Japanese).
To start the war Japan required about 10mil tons of shipping, in Dec 1941 she found herself with about 6.4 under control. 2mil were taken by the Army to invade the Philippines, another 2 were taken to support existing navy operations, meaning that already the Japanese economy was running on 25% of what they really needed to keep going full blast.
During the planning for Midway some naval officers thought they wouldn't even be able to keep them supplied if they took the island.
The other consideration was how in the Hell they would have been to get all the ships to Oahu in the first place. Just getting Kido Butai there without running out of fuel took almost every oiler that could be found. It was so closely run that Admiral Yamaguchi even suggested letting the escort destroyers run out of fuel and get towed back to ensure the carriers had enough to be safe. It is hard to imagine finding the way to get both sufficient transports there, and enough fuel for Kido Butai to remain on station.
This also assumes the Army somehow gave out 3 divisions when they barely gave out that many troops for the entirety of the Southern Offensive. They simply did not care about the Pacific, it was the Navy's fight, and had to be almost forced to give even a single regiment at Midway. To say nothing of the fact that Japan had 0 doctrine for conducting opposed landings, gunfire support, or CAS from her carriers. They had built a wonderful raiding force, but it was not capable of the same sustained offensive that the US Fast Carrier Force would be.