Inversion in an algebra of singular integral operators of generalized homogeneity David Weiland 42B20singular integrals A result of M. Christ on inversion of translation-invariant homogeneous singular integral operators on a Lie group having kernels with Sobolev-type smoothness is shown to hold without the homogeneity assumption. Instead we impose uniform size and smoothness conditions on the dilates of the kernel over a fixed annulus. These are analogous to the H\"{o}rmander condition for multipliers. Using natural embeddings between Sobolev and Lipschitz spaces we show that this generalization gives an inversion result for singular integral operators satisfying the standard Calder\'on-Zygmund Lipschitz estimates. Applications to the algebra of operators bounded on a Banach space of molecules are also given. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3430 10.1512/iumj.2008.57.3430 en Indiana Univ. Math. J. 57 (2008) 1235 - 1260 state-of-the-art mathematics http://iumj.org/access/