Multidimensional Singular Integrals and Integral Equations

Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics. Content: Front Matter, Page iii Copyright, Page iv DEDICATION, Page v PREFACE, Pages xi-xii CHAPTER I - INTRODUCTION, Pages 1-36 CHAPTER II - SIMPLEST PROPERTIES OF MULTIDIMENSIONAL SINGULAR INTEGRALS, Pages 37-62 CHAPTER III - COMPOUNDING OF SINGULAR INTEGRALS, Pages 63-92 CHAPTER IV - PROPERTIES OF THE SYMBOL, Pages 93-115 CHAPTER V - SINGULAR INTEGRALS IN Lp SPACES, Pages 116-133 CHAPTER VI - FURTHER INVESTIGATION OF THE SYMBOL, Pages 134-156 CHAPTER VII - SINGULAR INTEGRAL EQUATIONS, Pages 157-198 CHAPTER VIII - MISCELLANEOUS APPLICATIONS, Pages 199-224 APPENDIX - MULTIPLIERS OF FOURIER INTEGRALS, Pages 225-240 BIBLIOGRAPHY, Pages 241-249 INDEX, Pages 251-255 OTHER TITLES IN THE SERIES IN PURE AND APPLIED MATHEMATICS, Pages 257-259