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Anotace knihy

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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Zařazení knihy Knihy v angličtině Mathematics & science Mathematics Mathematical foundations

• Plný název: Weighted Morrey Spaces
• Podnázev: Calderón-Zygmund Theory and Boundary Problems
• Autor: Marcus Laurel, Marius Mitrea
• Jazyk: Angličtina
• Vazba: Pevná
• Počet stran: 480
• EAN: 9783111458168
• ID: 45923368
• Nakladatelství: De Gruyter
• Rozměry: 240 × 170 mm
• Datum vydání: 19. September 2024

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