Geometric Harmonic Analysis I

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.
Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense.
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.
Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense.
Includes chapter-level summaries Features novel principal results in monograph format Contains applications to complex analysis, scattering, and PDEs

Autor*in

Dorina Mitrea

Themen in »Geometric Harmonic Analysis I«

Divergence theorem Gauss-Green theorem Stokes theorem nontangential maximal function nontangentially accessible boundary Ahlfors regular domain NTA domain uniform domain Reifenberg flat domain regular SKT domain Riemannian manifold differential forms Hardy-Littlewood maximal function quasi-metric spaces spaces of homogenous type

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“The theory is developed in a consistent manner, and the motivation behind the results and tools is made clear to the reader. All of the main results and also a vast majority of the auxiliary results come with full and carefully written proofs, making the book highly self-contained. Thus this work can be a useful and enjoyable reference. …” (Juha Lehrbäck, Mathematical Reviews, August, 2024)

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