Norm Estimates for the $$\bar{\partial }$$-Equation on a Non-reduced Space

Abstract

We study norm-estimates for the $$\bar{\partial }$$ ∂ ¯ -equation on non-reduced analytic spaces. Our main result is that on a non-reduced analytic space, which is Cohen–Macaulay and whose underlying reduced space is smooth, the $$\bar{\partial }$$ ∂ ¯ -equation for (0, 1)-forms can be solved with $$L^p$$ L p -estimates.