Bøger i Lecture Notes in Mathematics serien

The book systematically develops the nonlinear potential theory connected with the weighted Sobolev spaces, where the weight usually belongs to Muckenhoupt's class of Ap weights. Applications of potential theory to weighted Sobolev spaces include quasi continuity of Sobolev functions, Poincare inequalities, and spectral synthesis theorems.

The 2nd edition of LNM 523 is based on the two first authors' mathematical approach of this theory presented in its 1st edition in 1976. Except for this new chapter and the correction of a few misprints, the basic material and presentation of the first edition has been maintained.

The 13 chapters of this book centre around the proof ofTheorem 1 of Faltings' paper "Diophantine approximation onabelian varieties", Ann. Eachchapter is based on an instructional lecture given by itsauthor ata special conference for graduate students, on thetopic of Faltings' paper.

Lectures given at the Banach Center and C.I.M.E. Joint Summer School held in Bedlewo, PolandSeptember 4-9, 2006

Lectures Given at the Inter-University Center of Postgraduate Studies, Dubrovnik, Yugoslavia, November 3-17, 1985

This book, now in its 2nd edition, is devoted to the arithmetical theory of Siegel modular forms and their L-functions.

The book is about differentiability of six operators on functions or pairs of functions: composition (f of g), integration (of f dg), multiplication and convolution of two functions, both varying, and the product integral and inverse operators for one function.