De Gruyter Weighted Morrey Spaces: Calderon-Zygmund Theory

Explore advanced mathematical analysis with this monograph from De Gruyter Studies in Mathematics. This work focuses on the effectiveness of singular integrals of layer potential type for solving boundary value problems. It specifically addresses weakly elliptic systems within the framework of Muckenhoupt-weighted Morrey spaces and their pre-duals. This text builds a functional analytic framework for Muckenhoupt-weighted Morrey spaces from the ground up, utilizing the rough setting of Ahlfors regular sets. It further extends this to support a Calderon-Zygmund theory in the optimal geometric environment of uniformly rectifiable sets. For researchers and mathematicians, this book provides a deep dive into duality theory for these specific Morrey spaces, offering a rigorous approach to complex boundary problems.