This volume presents advances that have been made over recent decades in
areas of research featuring Hardy's inequality and related topics. The
inequality and its extensions and refinements are not only of intrinsic
interest but are indispensable tools in many areas of mathematics and
mathematical physics.
Hardy inequalities on domains have a substantial role and this
necessitates a detailed investigation of significant geometric
properties of a domain and its boundary. Other topics covered in this
volume are Hardy- Sobolev-Maz'ya inequalities; inequalities of
Hardy-type involving magnetic fields; Hardy, Sobolev and
Cwikel-Lieb-Rosenbljum inequalities for Pauli operators; the Rellich
inequality.
The Analysis and Geometry of Hardy's Inequality provides an up-to-date
account of research in areas of contemporary interest and would be
suitable for a graduate course in mathematics or physics. A good basic
knowledge of real and complex analysis is a prerequisite.