{"product_id":"geometric-harmonic-analysis-i-dorina-mitrea-9783031059490","title":"Geometric Harmonic Analysis I: A Sharp Divergence Theorem with Nontangential Pointwise Traces","description":"Prefacing this Series.- Statement of Main Results Concerning the Divergence Theorem.- Examples, Counterexamples, and Additional Perspectives.- Measure Theoretical and Topological Rudiments.- Sets of Locally Finite Perimeter and Other Categories of Euclidean Sets.- Tools from Harmonic Analysis.- Quasi-Metric Spaces and Spaces of Homogenous Type.- Open Sets with Locally Finite Surface Measures and Boundary Behavior.- Proofs of Main Results Pertaining to the Divergence Theorem.- II: Function Spaces Measuring Size and Smoothness on Rough Sets.- Preliminary Functional Analytic Matters.- Selected Topics in Distribution Theory.- Hardy Spaces on Ahlfors Regular Sets.- Morrey-Campanato Spaces, Morrey Spaces, and Their Pre-Duals on Ahlfors Regular Sets.- Besov and Triebel-Lizorkin Spaces on Ahlfors Regular Sets.- Boundary Traces from Weighted Sobolev Spaces in Besov Spaces.- Besov and Triebel-Lizorkin Spaces in Open Sets.- Strong and Weak Normal Boundary Traces of Vector Fields in Hardy and Morney Spaces.- Sobolev Spaces on the Geometric Measure Theoretic boundary of Sets of Locally Finite Perimeter.- III: Integral Representations Calder-Zygmund Theory, Fatou Theorems, and Applications to Scattering.- Integral Representations and Integral Identities.- Calder-Zygmund Theory on Uniformly Rectifiable Sets.- Quantitative Fatou-Type Theorems in Arbitrary UR Domains.- Scattering by Rough Obstacles.- IV: Boundary Layer Potentials on Uniformly Rectifiable Domains, and Applications to Complex Analysis.- Layer Potential Operators on Lebesgue and Sobolev Spaces.- Layer Potential Operators on Hardy, BMO, VMO, and Hder Spaces.- Layer Potential Operators on Calder, Morrey-Campanato, and Morrey Spaces.- Layer Potential Operators Acting from Boundary Besov and Triebel-Lizorkin Spaces.- Generalized double Layers in Uniformly Rectifiable Domains.- Green Formulas and Layer Potential Operators for the Stokes System.- Applications to Analysis in Several Complex Variables.- V: Fredholm Theory and Finer Estimates for Integral Operators, with Applications to Boundary Problems.- Abstract Fredholm Theory.- Distinguished Coefficient Tensors.- Failure of Fredholm Solvability for Weakly Elliptic Systems.- Quantifying Global and Infinitesimal Flatness.- Norm Estimates and Invertibility Results for SIO's on Unbounded Boundaries.- Estimating Chord-Dot-Normal SIO's on Domains with Compact Boundaries.- The Radon-Carleman Problem.- Fredholmness and Invertibility of Layer Potentials on Compact Boundaries.- Green Functions and Uniqueness for Boundary Problems for Second-Order Systems.- Green Functions and Poisson Kernels for the Laplacian.- Boundary Value Problems for Elliptic Systems in Rough Domains.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Dorina Mitrea, Irina Mitrea, Marius Mitrea\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 3031059492\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9783031059490\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Springer\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 11\/05\/2022\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 924\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Hardcover\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 3.30lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.21h x 6.14w x 1.94d","brand":"Dorina Mitrea","offers":[{"title":"Hardcover","offer_id":44069277401343,"sku":"9783031059490","price":199.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_bdd7186e-359b-490f-a3a6-462e4c310432.jpg?v=1685423827","url":"https:\/\/www.whiterainbookhouse.com\/products\/geometric-harmonic-analysis-i-dorina-mitrea-9783031059490","provider":"WR Book House","version":"1.0","type":"link"}