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 Oxford, Courant Institute, Max-Planck-Institute Leipzig and Warwick. He heads up the Analysis and PDEs research group in Sussex In June 2014 he was awarded the First University of Sussex Student Led Teaching Prize for "Outstanding and Innovative Postgraduate Teaching in Mathematics".

• 13: Maximal Function; Bounding Averages and Pointwise Convergence


• 14: Harmonic-Hardy Spaces hp(H)


• 15: Sobolev Spaces; A Resolution of the Dirichlet Principle


• 16: Singular Integral Operators and Vector-Valued Inequalities


• 17: Littlewood-Paley Theory, Lp-Multipliers and Function Spaces


• 18: Morrey and Campanato vs. Hardy and John-Nirenberg Spaces


• 19: Layered Potentials, Jump Relations and Existence Theorems


• 20: Second Order Equations in Divergence Form: Continuous Coefficients


• 21: Second Order Equations in Divergence Form: Measurable Coefficients


• A: Partition of Unity


• B: Total Boundedness and Compact Subsets of Lp


• C: Gamma and Beta Functions


• D: Volume of the Unit n-Ball


• E: Integrals Related to Abel and Gauss Kernels


• F: Hausdorff Measures Hs


• G: Evaluation of Some Integrals Over


• H: Sobolev Spaces

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.