Geometric Harmonic Analysis IV
Boundary Layer Potentials in Uniformly Rectifiable Domains, and Applications to Complex Analysis
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Beschreibung
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 mapping 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.
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 mapping 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.
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
Autor*in
Dorina Mitrea
Themen in »Geometric Harmonic Analysis IV«
Divergence theorem integration by parts Stokes theorem singular integral operators function spaces boundary value problems integral representation formulas in complex analysis
Stimmen zu »Geometric Harmonic Analysis IV«
“The monograph is very well written, and the results are deep. In the reviewer's opinion, the book is a valuable reference for all those who are interested in potential theory and boundary value problems in domains of quite general geometric nature.” (Paolo Musolino, Mathematical Reviews, August, 2024)
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