  In this work, we generalise the stochastic local time space integration
introduced in \cite{Ei00} to the case of Brownian sheet. %We develop a
stochastic local time-space calculus with respect to the Brownian sheet. This
allows us to prove a generalised two-parameter It\^o formula and derive Davie
type inequalities for the Brownian sheet. Such estimates are useful to obtain
regularity bounds for some averaging type operators along Brownian sheet
curves.
