The subject of this book is the interplay between function space theory and potential theory. The theory has reached a state of maturity and elegance by now that makes it natural to present it in book form. The book is accessible to graduate students with a good background in real analysis. No previous knowlegde of potential theory is assumed.

Pr�sentation de l'�diteur

The subject of this book is the interplay between function space theory and potential theory. A crucial step in classical potential theory is the identification of the potential energy of a charge with the square of a Hilbert space norm. This leads to the Dirichlet space of locally integrable functions whose gradients are square integrable. More recently, a generalized potential theory has been developed, which has an analogous relationship to the standard Banach function spaces, Sobolev spaces, Besov spaces etc., that appear naturally in the study of partial differential equations. A surprisingly large part of classical potential theory has been extended to this nonlinear setting. The extensions are sometimes surprising, usually they are nontrivial and have required new methods.

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