Weighted Morrey Spaces Calderón-Zygmund Theory and Boundary Problems
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Form:Einzelkauf Download
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Sprache:Englisch
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eBook Format:PDF
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Produktdetails
Format
Kopierschutz
Nein
Family Sharing
Ja
Text-to-Speech
Nein
Erscheinungsdatum
03.09.2024
Verlag
Walter de Gruyter GmbH & Co.KGSeitenzahl
432 (Printausgabe)
Dateigröße
7270 KB
Auflage
1. Auflage
Sprache
Englisch
EAN
9783111458274
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.
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