Gaussian Capacity Analysis, 1st ed. 2018 Lecture Notes in Mathematics Series, Vol. 2225

This monograph develops the Gaussian functional capacity theory with applications to restricting the Gaussian Campanato/Sobolev/BV space. Included in the text is a new geometric characterization of the Gaussian 1-capacity and the Gaussian Poincaré 1-inequality.  Applications to function spaces and geometric measures are also presented.

This book will be of use to researchers who specialize in potential theory, elliptic differential equations, functional analysis, probability, and geometric measure theory. 

The first book presenting a systematic study of the Sovolev/BV capacity theory in the Gaussian setting

Provides fundamental material for a cross-disciplinary field

Provides interesting applications in the geometry of Gaussian space