Weighted Morrey Spaces

Calderón-Zygmund Theory and Boundary Problems

von Marcus Laurel, Marius Mitrea

426 Seiten, Hardcover

Kurzbeschreibung des Verlags

This monograph is a testament to the potency of the method of singular integrals of layer potential type in solving boundary value problems for weakly elliptic systems in the setting of Muckenhoupt-weighted Morrey spaces and their pre-duals.

A functional analytic framework for Muckenhoupt-weighted Morrey spaces in the rough setting of Ahlfors regular sets is built from the ground up and subsequently supports a Calderón-Zygmund theory on this brand of Morrey space in the optimal geometric environment of uniformly rectifiable sets. A thorough duality theory for such Morrey spaces is also developed and ushers in a never-before-seen Calderón-Zygmund theory for Muckenhoupt-weighted Block spaces. Both weighted Morrey and Block spaces are also considered through the lens of (generalized) Banach function spaces, and ultimately, a variety of boundary value problems are formulated and solved with boundary data arbitrarily prescribed from either scale of space.

The fairly self-contained nature of this monograph ensures that graduate students, researchers, and professionals in a variety of fields, e.g., function space theory, harmonic analysis, and PDE, will find this monograph a welcome and valuable addition to the mathematical literature.

• Reihe: De Gruyter Studies in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Mathematische Analysis, allgemein Funktionalanalysis und Abwandlungen
• ISBN: 9783111458168
• Sprache: Englisch
• Erscheinungsdatum: 03.09.2024
• Größe: 24 x 17 cm
• Verlag: De Gruyter