" This volume contains the expanded lecture notes of courses taught at the Emile Borel
Centre of the Henri Poincaré Institute (Paris). In the book, leading experts introduce recent …

6.3 Non-uniform change of measure 141 6.4 Conformal change of the metric tensor 144 6.5
Manifolds with ends 147 7. Eigenvalues of Schrödinger operators 149 7.1 Negative …

" The book describes how functional inequalities are often manifestations of natural
mathematical structures and physical phenomena, and how a few general principles …

This book discusses advances in maximal function methods related to Poincaré and
Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy's …

Hardy-type inequalities related to degenerate elliptic differential operators Page 1 Ann. Scuola
Norm. Sup. Pisa Cl. Sci. (5) Vol. IV (2005), 451-486 Hardy-type inequalities related to …

We consider Hardy–Rellich inequalities and discuss their possible improvement. The
procedure is based on decomposition into spherical harmonics, where in addition various …

In this paper, we study classical Hardy inequalities, both in the subcritical case on the whole
space and the critical case on a ball. Two Hardy inequalities are quite different from each …

We present a new form of the logarithmic Hardy inequality on the unit ball in with its optimal
constant. One of the novelties of our inequality is the scale invariance under the natural …

We study Hardy-type inequalities associated to the quadratic form of the shifted Laplacian−
Δ HN−(N− 1) 2/4 on the hyperbolic space HN,(N− 1) 2/4 being, as it is well-known, the …

We prove optimal improvements of the Hardy inequality on the hyperbolic space. Here,
optimal means that the resulting operator is critical in the sense of Devyver, Fraas, and …