Open Daily: 10am - 10pm | Alley door pickup 10am - 7pm 3038 Hennepin Ave Minneapolis, MN
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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Weighted Morrey Spaces: Calderón-Zygmund Theory and Boundary Problems

Weighted Morrey Spaces: Calderón-Zygmund Theory and Boundary Problems

Mitrea, Marius
Laurel, Marcus

Hardcover

Series: de Gruyter Studies in Mathematics, Book 99

FictionGeneral MathematicsGeometry

ISBN10: 3111458164
ISBN13: 9783111458168
Publisher: de Gruyter
Published: Sep 3 2024
Pages: 432
Weight: 1.95
Height: 0.94 Width: 6.69 Depth: 9.61
Language: English

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.

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