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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.
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.
| Erscheinungsjahr: | 2024 |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
VI
426 S. 2 s/w Illustr. 2 b/w ill. |
| ISBN-13: | 9783111458168 |
| ISBN-10: | 3111458164 |
| Sprache: | Englisch |
| Autor: |
Laurel, Marcus
Mitrea, Marius |
| Hersteller: | De Gruyter |
| Abbildungen: | 2 b/w ill. |
| Maße: | 27 x 178 x 242 mm |
| Von/Mit: | Marcus Laurel (u. a.) |
| Erscheinungsdatum: | 03.09.2024 |
| Gewicht: | 0,85 kg |
| Erscheinungsjahr: | 2024 |
|---|---|
| Genre: | Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Buch |
| Inhalt: |
VI
426 S. 2 s/w Illustr. 2 b/w ill. |
| ISBN-13: | 9783111458168 |
| ISBN-10: | 3111458164 |
| Sprache: | Englisch |
| Autor: |
Laurel, Marcus
Mitrea, Marius |
| Hersteller: | De Gruyter |
| Abbildungen: | 2 b/w ill. |
| Maße: | 27 x 178 x 242 mm |
| Von/Mit: | Marcus Laurel (u. a.) |
| Erscheinungsdatum: | 03.09.2024 |
| Gewicht: | 0,85 kg |
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