Multidimensional Singular Integrals and Integral Equations

PrefaceI. Introduction § 1. Review of Previous Work § 2. Some Theorems on Linear Equations in Banach Spaces § 3. Stereographic Projection § 4. Completely Continuous OperatorsII. Simplest Properties of Multidimensional Singular Integrals § 5. Basic Concepts § 6. Lipschitz Conditions § 7. Order of Singular Integrals at Infinity § 8. Differentiation of Integrals with a Weak SingularityIII. Compounding of Singular Integrals § 9. Compounding of Singular and Ordinary Integrals § 10. Compounding of Double Singular Integrals § 11. The Concept of a Singular Operator § 12. Compounding of Double Singular Integrals. The Symbol § 13. Compounding of Multidimensional Singular Integrals § 14. Formulae for Reference § 15. Product of the Operators A1 and An § 16. Product of the Operators A2 and An § 17. Calculation of x1,m § 18. Symbol of a Multidimensional Singular IntegralIV. Properties of the Symbol § 19. Fourier Transform of a Singular Kernel § 20. Fourier Transform of a Kernel and the Symbol of a Singular Operator § 21. Transformation of the Symbol Under Change of Variables § 22. Differentiability of the Symbol § 23. The Conditions for the Continuity of the SymbolV. Singular Integrals in Lp Spaces § 24. The Simplest Corollaries from the Fourier Transform. First Theorem on Boundedness in L2 Space § 25. Symbol Dependent on the Pole. Second Theorem on Boundedness in L2 Space § 26. On the Boundedness of a Singular Integral Operator in Lp Space § 27. Integrals Taken Over any Manifold § 28. Differential Properties of Singular IntegralsVI. Further Investigation of the Symbol § 29. More About the Differentiation of Integrals with a Weak Singularity § 30. Polyharmonic Potentials § 31. Series of Spherical Functions § 32. Differential Properties of the Symbol and the Characteristic § 33. Rule for the Multiplication of the Symbols in the General Case § 34. Conjugate Singular OperatorVII. Singular Integral Equations § 35. The Case Where the Symbol is Independent of the Pole § 36. The Case Where the Symbol is Dependent on pole. Regularization and Domains of Constancy of the Index § 37. Equivalent Regularization. Index Theorem § 38. Equations with an Integral Taken Over a Closed Manifold § 39. Extension by Means of the Parameter § 40. Systems of Singular Integral Equations § 41. Singular Integral Equations in Classes of Lipschitz FunctionsVIII. Miscellaneous Applications § 42. Leading Derivatives of Volume Potential § 43. Problem of the Oblique Derivative § 44. Inequality Involving the Tangential and Normal Components of the Gradient of a Harmonic Function § 45. Equilibrium of an Isotropic Elastic Body § 46. Diffraction of Stationary Elastic WavesAppendix. Multipliers of Fourier IntegralsBibliographyIndexOther Titles in the Series