Subaveraging estimate for 𝐶𝑅 functions defined on a hypersurface 𝑀 of 𝐶ⁿ

Paolantoni, Victoria

doi:10.1090/S0002-9939-98-04466-9

Subaveraging estimate for $CR$ functions defined on a hypersurface $M$ of ${\mathrm {C}}^{n}$
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Proc. Amer. Math. Soc. 126 (1998), 1733-1738 Request permission

Abstract:

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 $M$.

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