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-Mazya 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 Hardys 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.
Hardy, Sobolev, and CLR inequalities.- Boundary curvatures and the distance function.- Hardy's inequality on domains.- Hardy, Sobolev, Maz'ya (HSM) inequalities.- Inequalities and operators involving magnetic elds.- The Rellich inequality.
This book is the epitome of classical analysis andhas been a staple of those who have wished to learn that art since CambridgeUniversity Press published it in 1934. & The terseness of the developmentthroughout make this book more suitable for graduate students. All in all, thebook under review is a lovely compendium of the utility and power of HardysInequality. (Jeff Ibbotson, MAA Reviews, maa.org, January, 2016)
Alexander Balinsky is Professor of Mathematical Physics in the School of Mathematics at Cardiff University. His wide interests include spectral problems for the differential operators of mathematical physics, and currently, the mathematics of image processing, machine lSą
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