SpringerLink
Log in

Geometric Harmonic Analysis IV

Boundary Layer Potentials in Uniformly Rectifiable Domains, and Applications to Complex Analysis

  • Book
  • © 2023

Overview

Authors:
  1. Dorina Mitrea

    1. Department of Mathematics, Baylor University, Waco, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Irina Mitrea

    1. Department of Mathematics, Temple University, Philadelphia, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  3. Marius Mitrea

    1. Department of Mathematics, Baylor University, Waco, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Current theory of layer potentials for elliptic systems in optimal settings for a wealth of function spaces
  • Detailed account of relevant boundary layer operators for Stokes’ system of hydrostatics in optimal settings
  • Blurs the boundaries between geometric measure theory, several complex variables, and Calderón-Zygmund theory

Part of the book series: Developments in Mathematics (DEVM, volume 75)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook EUR 128.39
Price includes VAT (Germany)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book EUR 171.19
Price includes VAT (Germany)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free ship** worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

About this book

This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations.

Traditionally, the label “Calderón-Zygmund theory” has been applied to a distinguished body of works primarily pertaining to the map** properties of singular integral operators on Lebesgue spaces, in various geometric settings. Volume IV amounts to a versatile Calderón-Zygmund theory for singular integral operators of layer potential type in open sets with uniformly rectifiable boundaries, considered on a diverse range of function spaces. Novel applications to complex analysis in several variables are also explored here.


Keywords

Table of contents (8 chapters)

  1. Front Matter

    Pages i-xix
    Download chapter PDF

  2. Layer Potential Operators on Lebesgue and Sobolev Spaces

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 1-233

  3. Layer Potential Operators on Hardy, BMO, VMO, and Hölder Spaces

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 235-374

  4. Layer Potential Operators on Calderón, Morrey-Campanato, and Morrey Spaces

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 375-427

  5. Layer Potential Operators Acting from Boundary Besov and Triebel-Lizorkin Spaces

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 429-530

  6. Generalized Double Layers in Uniformly Rectifiable Domains

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 531-672

  7. Green Formulas and Layer Potential Operators for the Stokes System

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 673-781

  8. Applications to Analysis in Several Complex Variables

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 783-882

  9. Hardy Spaces for Second-Order Weakly Elliptic Operators in the Complex Plane

    • Dorina Mitrea, Irina Mitrea, Marius Mitrea
    Pages 883-922

  10. Back Matter

    Pages 923-992
    Download chapter PDF
Back to top

Authors and Affiliations

  • Department of Mathematics, Baylor University, Waco, USA

    Dorina Mitrea, Marius Mitrea

  • Department of Mathematics, Temple University, Philadelphia, USA

    Irina Mitrea

Bibliographic Information

  • Book Title: Geometric Harmonic Analysis IV

  • Book Subtitle: Boundary Layer Potentials in Uniformly Rectifiable Domains, and Applications to Complex Analysis

  • Authors: Dorina Mitrea, Irina Mitrea, Marius Mitrea

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/978-3-031-29179-1

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023

  • Hardcover ISBN: 978-3-031-29178-4Published: 10 July 2023

  • Softcover ISBN: 978-3-031-29181-4Due: 10 August 2023

  • eBook ISBN: 978-3-031-29179-1Published: 09 July 2023

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: XIX, 992

  • Number of Illustrations: 1 b/w illustrations

  • Topics: Integral Transforms, Operational Calculus

Publish with us

Policies and ethics

Back to top

Search

Navigation