Subaveraging estimate for $CR$ functions defined on a hypersurface $M$ of ${\mathrm{C}}^{n}$

Let $M$ be a smooth real hypersurface of $\mathrm{C}^{n}$ and $N$ a compact submanifold of $M$. We generalize a result of A. Boggess and R. Dwilewicz giving, under some geometric conditions on $M$ and $N$, an estimate of the submeanvalue on $N$ of any $CR$ function $f$ on a neighbourhood of $N$, by the $L^{1}$ norm of $f$ on a neighbourhood of $N$ in $M$.