Weak hypotheses in the boosting method

I'm assuming you mean weak classifiers that go together in boosting? Often these are decision trees for only a few layers. They are trained one by one on a dataset weighted in such a way that the data indicates that the last classifier received the wrong values, giving more weight.

Read these notes from the UPenn Machine Learning Class for more information:

http://alliance.seas.upenn.edu/~cis520/wiki/index.php?n=Lectures.Boosting