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Weighted Morrey Spaces

2024-09-02 Mathematics
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Release : 2024-09-02
Genre : Mathematics
Kind : eBook
Book Rating : 459/5 ( reviews)

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Book Synopsis Weighted Morrey Spaces by : Marcus Laurel

Download or read book Weighted Morrey Spaces written by Marcus Laurel. This book was released on 2024-09-02. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Weighted Morrey Spaces

2024-09-23 Mathematics
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Release : 2024-09-23
Genre : Mathematics
Kind : eBook
Book Rating : 168/5 ( reviews)

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Book Synopsis Weighted Morrey Spaces by : Marcus Laurel

Download or read book Weighted Morrey Spaces written by Marcus Laurel. This book was released on 2024-09-23. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Morrey Spaces

2020-09-16 Mathematics
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Release : 2020-09-16
Genre : Mathematics
Kind : eBook
Book Rating : 077/5 ( reviews)

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Book Synopsis Morrey Spaces by : Yoshihiro Sawano

Download or read book Morrey Spaces written by Yoshihiro Sawano. This book was released on 2020-09-16. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume II focused mainly generalizations and interpolation of Morrey spaces. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

Morrey Spaces

2020-09-16 Mathematics
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Release : 2020-09-16
Genre : Mathematics
Kind : eBook
Book Rating : 521/5 ( reviews)

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Book Synopsis Morrey Spaces by : Yoshihiro Sawano

Download or read book Morrey Spaces written by Yoshihiro Sawano. This book was released on 2020-09-16. Available in PDF, EPUB and Kindle. Book excerpt: Morrey spaces were introduced by Charles Morrey to investigate the local behaviour of solutions to second order elliptic partial differential equations. The technique is very useful in many areas in mathematics, in particular in harmonic analysis, potential theory, partial differential equations and mathematical physics. Across two volumes, the authors of Morrey Spaces: Introduction and Applications to Integral Operators and PDE’s discuss the current state of art and perspectives of developments of this theory of Morrey spaces, with the emphasis in Volume I focused mainly on harmonic analysis. Features Provides a ‘from-scratch’ overview of the topic readable by anyone with an understanding of integration theory Suitable for graduate students, masters course students, and researchers in PDE's or Geometry Replete with exercises and examples to aid the reader’s understanding

On Some Results in Weighted Morrey Spaces with Applications to PDE

2012
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Release : 2012
Genre :
Kind : eBook
Book Rating : /5 ( reviews)

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Book Synopsis On Some Results in Weighted Morrey Spaces with Applications to PDE by : Lars-Erik Persson

Download or read book On Some Results in Weighted Morrey Spaces with Applications to PDE written by Lars-Erik Persson. This book was released on 2012. Available in PDF, EPUB and Kindle. Book excerpt:

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