  In this paper, we show that the kernel function of Cauchy type for type $BC$
intertwines the commuting family of van Diejen's $q$-difference operators. This
result gives rise to a transformation formula for certain multiple basic
hypergeometric series of type $BC$. We also construct a new infinite family of
commuting $q$-difference operators for which the Koornwinder polynomials are
joint eigenfunctions.
