JAPANESE investment in the territory is booming, with investors showing little concern about either their domestic economic difficulties or the handover to China in 1997, a survey of Japanese firms in Hong Kong has shown. According to Japan's Ministry of Finance, investment over the past fiscal year increased by 68 per cent to US$1.2 billion. Total investment in Hong Kong and China over the period accounted for $2.9 billion - or about eight per cent of Japan's total investment abroad. Another 135 companies moved into Hong Kong last year, taking the total to 1,796. The survey of 240 companies said: ''The firms are generally anticipating business opportunities and they are optimistic about the economic future of Hong Kong and southern China beyond 1997.'' About 40 per cent of the companies surveyed were considering increasing their investment. But the survey found that many companies setting up businesses in China were ''facing a barrier of peculiar and traditional business customs in the personal network society of China.''