Multidimensional Singular Integrals and Integral Equations

Contents......Page all_21026_to_00269.cpc0005.djvu Preface......Page all_21026_to_00269.cpc0009.djvu §1. Review of previous work......Page all_21026_to_00269.cpc0011.djvu §2. Some theorems on linear equations in Banach spaces......Page all_21026_to_00269.cpc0031.djvu §3. Stereographic projection......Page all_21026_to_00269.cpc0040.djvu §4. Completely continuous operators......Page all_21026_to_00269.cpc0042.djvu §5. Basic concepts......Page all_21026_to_00269.cpc0047.djvu §6. Lipschitz conditions......Page all_21026_to_00269.cpc0056.djvu §7. Order of singular integrals at infinity......Page all_21026_to_00269.cpc0060.djvu §8. Differentiation of integrals with a weak singularity......Page all_21026_to_00269.cpc0069.djvu §9. Compounding of singular and ordinary integrals......Page all_21026_to_00269.cpc0073.djvu §10. Compounding of double singular integrals......Page all_21026_to_00269.cpc0077.djvu §11. The concept of a singular operator......Page all_21026_to_00269.cpc0080.djvu §12. Compounding of double singular integrals. The symbol......Page all_21026_to_00269.cpc0081.djvu §13. Compounding of multidimensional singular integrals......Page all_21026_to_00269.cpc0082.djvu §14. Formulae for reference......Page all_21026_to_00269.cpc0084.djvu §15. Product of the operators A_1 and A_n......Page all_21026_to_00269.cpc0087.djvu §16. Product of the operators A_2 and A_n......Page all_21026_to_00269.cpc0091.djvu §17. Calculation of \kappa_{1,m}......Page all_21026_to_00269.cpc0093.djvu §18. Symbol of a multidimensional singular integral......Page all_21026_to_00269.cpc0096.djvu §19. Fourier transform of a singular kernel......Page all_21026_to_00269.cpc0103.djvu §20. Fourier transform of a kernel and the symbol of a singular operator......Page all_21026_to_00269.cpc0107.djvu §21. Transformation of the symbol under change of variables......Page all_21026_to_00269.cpc0114.djvu §22. Differentiability of the symbol......Page all_21026_to_00269.cpc0119.djvu §23. The conditions for the continuity of the symbol......Page all_21026_to_00269.cpc0122.djvu §24. The simplest corollaries from the Fourier transform. First theorem on boundedness in L_2 space......Page all_21026_to_00269.cpc0126.djvu §25. Symbol dependent on the pole. Second theorem on boundedness in L_2 space......Page all_21026_to_00269.cpc0129.djvu §26. On the boundedness of a singular integral operator in L_p space......Page all_21026_to_00269.cpc0133.djvu §27. Integrals taken over any manifold......Page all_21026_to_00269.cpc0140.djvu §28. Differential properties of singular integrals......Page all_21026_to_00269.cpc0141.djvu §29. More about the differentiation of integrals with a weak singularity......Page all_21026_to_00269.cpc0144.djvu §30. Polyharmonic potentials......Page all_21026_to_00269.cpc0145.djvu §31. Series of spherical functions......Page all_21026_to_00269.cpc0146.djvu §32. Differential properties of the symbol and the characteristic......Page all_21026_to_00269.cpc0158.djvu §33. Rule for the multiplication of the symbols in the general case......Page all_21026_to_00269.cpc0160.djvu §34. Conjugate singular operator......Page all_21026_to_00269.cpc0164.djvu §35. The case where the symbol is independent of the pole......Page all_21026_to_00269.cpc0167.djvu §36. The case where the symbol is dependent on pole. Regularization and domains of constancy of the index......Page all_21026_to_00269.cpc0168.djvu §37. Equivalent regularization. Index theorem......Page all_21026_to_00269.cpc0170.djvu §38. Equations with an integral taken over a closed manifold......Page all_21026_to_00269.cpc0182.djvu §39. Extension by means of the parameter......Page all_21026_to_00269.cpc0190.djvu §40. Systems of singular integral equations......Page all_21026_to_00269.cpc0194.djvu §41. Singular integral equations in classes of Lipschitz functions......Page all_21026_to_00269.cpc0200.djvu §42. Leading derivatives of volume potential......Page all_21026_to_00269.cpc0209.djvu §43. Problem of the oblique derivative......Page all_21026_to_00269.cpc0213.djvu §44. Inequality involving the tangential and normal components of the gradient of a harmonic function......Page all_21026_to_00269.cpc0218.djvu §45. Equilibrium of an isotropic elastic body......Page all_21026_to_00269.cpc0220.djvu §46. Diffraction of stationary elastic waves......Page all_21026_to_00269.cpc0230.djvu Appendix. Multipliers of Fourier Integrals......Page all_21026_to_00269.cpc0235.djvu Bibliography......Page all_21026_to_00269.cpc0251.djvu Index......Page all_21026_to_00269.cpc0261.djvu Other Titles in the Series......Page all_21026_to_00269.cpc0267.djvu