  In this paper, we study joint functional calculus for commuting $n$-tuple of
Ritt operators. We provide an equivalent characterisation of boundedness for
joint functional calculus for Ritt operators on $L^p$-spaces, $1< p<\infty$. We
also investigate joint similarity problem and joint bounded functional calculus
on non-commutative $L^p$-spaces for $n$-tuple of Ritt operators. We get our
results by proving a suitable multivariable transfer principle between
sectorial and Ritt operators as well as an appropriate joint dilation result in
a general setting.
