*(English)*Zbl 0612.47024

The book is translated with some modifications from the German edition (1980; Zbl 0442.47027). It remains to indicate only the changes, incorporated by the translation.

In Chapter XI the new § 12 deals with the recent results on weighted norm inequalities for one-dimensional singular integral operators, due to R. Hunt. B. Muckenhoupt, R. Wheeden.

In Chapter XII the new § 7 is added, where polysingular integral operators with continuous coefficients are considered in the space ${L}_{p}\left({\mathbb{R}}^{2}\right)$ (results of I. Simonenko and V. Pilidi). In the same chapter § 8 deals with some basic notions for pseudo-differential operators in Sobolev-spaces ${W}_{2}^{\left(1\right)}\left({\mathbb{R}}^{m}\right)$ (the boundedness, composition formula, parametrix,...).

In Chapter XVII, § 3 two new subsections (3.6 and 3.7) deal with the polynomial approximation method for singular integral equations over a finite interval with discontinuous coefficients. In the same chapter the new § 4 describes the spline collocation method for a one-dimensional singular integral equation.

In many other places new results can be found that have appeared within the 5 years after the first edition. References are extended on 150 new items.

##### MSC:

47B35 | Toeplitz operators, Hankel operators, Wiener-Hopf operators |

47-02 | Research monographs (operator theory) |

45E05 | Integral equations with kernels of Cauchy type |

47Gxx | Integral, integro-differential, and pseudodifferential operators |

45P05 | Integral operators |