Function Spaces and Partial Differential Equations: Volume 2 - Contemporary Analysis

Hardcover | August 30, 2015

byAli Taheri

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This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the bookprimarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples,worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and facultyin mathematics worldwide have started their research career from the course that formed the basis for this book.

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From the Publisher

This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the bookprimarily lies in its clear and detailed explan...

Dr Taheri is a Reader in Mathematics as the University of Sussex. His primary research area is in the field of years. During which time he has published research papers in prestigious journals, made valuable contributions to the field and has taught and conducted research in some of the leading institutions in the world including Oxfo...

other books by Ali Taheri

Format:HardcoverDimensions:480 pages, 9.21 × 6.14 × 1.12 inPublished:August 30, 2015Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198733151

ISBN - 13:9780198733157

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Table of Contents

13. Maximal Function; Bounding Averages and Pointwise Convergence14. Harmonic-Hardy Spaces hp(H)15. Sobolev Spaces; A Resolution of the Dirichlet Principle16. Singular Integral Operators and Vector-Valued Inequalities17. Littlewood-Paley Theory, Lp-Multipliers and Function Spaces18. Morrey and Campanato vs. Hardy and John-Nirenberg Spaces19. Layered Potentials, Jump Relations and Existence Theorems20. Second Order Equations in Divergence Form: Continuous Coefficients21. Second Order Equations in Divergence Form: Measurable CoefficientsA. Partition of UnityB. Total Boundedness and Compact Subsets of LpC. Gamma and Beta FunctionsD. Volume of the Unit n-BallE. Integrals Related to Abel and Gauss KernelsF. Hausdorff Measures HsG. Evaluation of Some Integrals OverH. Sobolev Spaces