Titlebook: Geometric Harmonic Analysis III; Integral Representat Dorina Mitrea,Irina Mitrea,Marius Mitrea Book 2023 The Editor(s) (if applicable) and

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Book 2023aim 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 profession

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Quantitative Fatou-Type Theorems in Arbitrary UR Domains,elliptic equation in a certain domain implies the a.e. existence of the pointwise nontangential boundary trace of said function. It is natural to call such a theorem quantitative if the boundary trace does not just simply exist, but also encodes significant information regarding the size and regular

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Green Functions and Poisson Kernels for the Laplacian, by questions in potential theory for the Laplacian in . of the following sort: When is the Poisson kernel associated with a domain . (as the Radon-Nikodym derivative of the harmonic measure with respect to the surface measure) well-defined and equal to the (minus) normal derivative of the Green fun

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Quantitative Fatou-Type Theorems in Arbitrary UR Domains,nt .. Such a result has a wide range of applications, including the theory of Hardy spaces associated with injectively elliptic first-order systems in UR domains. Among other things, here we also prove a quantitative Fatou-type theorem for the gradient of null-solutions of second-order systems in UR

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