Titlebook: Geometric Harmonic Analysis II; Function Spaces Meas Dorina Mitrea,Irina Mitrea,Marius Mitrea Book 2022 The Editor(s) (if applicable) and T

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Physiatrist

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Hardy Spaces on Ahlfors Regular Sets,he usefulness and versatility of a brand of Hardy spaces which places minimal regularity and structural demands on the underlying space. Here we are concerned with Hardy spaces on Ahlfors regular subsets of the Euclidean ambient and, by further building on the work in [9], consider topics such as th

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Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors Regular Sets,ces (cf., e.g., [2], [6], [63], [117], [155], [157], [184] and the references therein). The goal here is to develop a theory for these scales of spaces, which is comparable in scope and power to its Euclidean counterpart, in more general geometric settings. To set the stage, throughout we let . (whe

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Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets,Euclidean setting. Here we are concerned with adaptations of these scales of spaces to more general ambients, which only enjoy but a small fraction of the structural richness of the Euclidean space. This is in line with efforts made in the direction of extending the standard theory of Besov and Trie

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Boundary Traces from Weighted Sobolev Spaces into Besov Spaces,Next, in §., we consider traces from weighted Sobolev spaces defined in a given .-domain . by relying on P. Jones’ extension theorem to reduce matters to the full Euclidean setting considered earlier. The next order of business is to construct extension operators from boundary Besov spaces into our

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Sobolev Spaces on the Geometric Measure Theoretic Boundary of Sets of Locally Finite Perimeter,ein), here the goal is to introduce a scale of Sobolev spaces on the geometric measure theoretic boundaries of sets of locally finite perimeter in the Euclidean setting and on Riemannian manifolds. This builds and expands on the work in [97], [139], and [141]. Our brand of “boundary” Sobolev spaces

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