Nonlinear multi-scale transforms: Lp theory

We treat the Lp theory ( 1 ≤ p < ∞ ) for univariate nonlinear subdivision schemes and multi-scale transforms based on the concept of offset invariance and nonlinear derived subdivision operators. The paper covers convergence, smoothness, and stability issues, and complements the recent survey [8], where results for Lp have been included without proof.