Weighted Morrey Spaces : Calderon-Zygmund Theory and Boundary Problems - Marcus Laurel - Books - De Gruyter - 9783111458168 - September 3, 2024
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Marcus Laurel
Weighted Morrey Spaces : Calderon-Zygmund Theory and Boundary Problems

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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.

Media Books     Hardcover Book   (Book with hard spine and cover)
Released September 3, 2024
ISBN13 9783111458168
Publishers De Gruyter
Pages 432
Dimensions 150 × 220 × 20 mm   ·   845 g

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