Question
I was considering growing a table/juice grape on an arbor attached to the wall of my south-facing house.  There is no shade, as my house is a passive solar construction.
In every reference I can find I learn that a) container grown grapevines will fruit little or not at all, and b) pollination is necessary.  Is the lack of fruit because the roots are restricted by the container or because pollination is somehow more difficult in container grown plants?

Answer
A plant will put its sources into survival first, and if growing conditions are not optimum, then fruiting will suffer; in this case, you are indeed restricting the area the roots can expand and this will definitely effect the growth of the crown and development of the plant in general. Grapes have a root system that runs and spreads and they need adequate room to do this. Pollination is not a factor, for insects will pollinate flowers, whether or not the plant/tree is contained, but if no flowers form, then no pollination is possible. Nick