  We construct and analyze the Jacobi process - in mathematical biology
referred to as Wright-Fisher diffusion - using a Dirichlet form. The
corresponding Dirichlet space takes the form of a Sobolev space with different
weights for the function itself and its derivative. Depending on the parameters
we characterize the boundary behavior of the functions in the Dirichlet space,
show density results, derive Sobolev embeddings and verify functional
inequalities of Hardy type. Since the generator is a hypergeometric
differential operator, many of the proofs can be carried out by explicit
calculations involving hypergeometric functions. We deduce corresponding
properties for the associated semigroup and Markov process and show that the
latter is up to minor technical modifications a solution to the Jacobi SDE.
