Abstract
Let U be a neighborhood of 0in ℂn, 1 ≤s ≤ n − 1,m ∈ ℕ,M = {(z1,..., zn) ∈ U:Imzn = ¦z1¦2 + ...¦zs¦2 + (¦zs+1¦2 +...+ ¦zn−1¦2)m +some error} term be a hypersurface in U. In this paper, the author constructs homotopy operators for the local tangential Cauchy-Riemann operator on the neighborhoods Mδ:= M ∩ {¦zn¦ < δ} of 0in M. C0 -estimates up to the boundary are proved for the operators. The constants in the estimates do not depend on δ.
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