Why bootstrapping for J-holomorphic curves fails in $$C^k$$

Abstract

AbstractWe present a simple example for the failure of the Calderón–Zygmund estimate for the $$\overline{\partial }$$ ∂ ¯ -operator when the Sobolev (k, p)-norms are replaced by the $$C^k$$ C k -norms. This example is discussed in the context of elliptic bootstrapping, Fredholm theory, and the regularity of J-holomorphic curves.