10 citations · 20 across the 12 of their papers we have counts for
13 papers
Sharp estimates and inequalities on Riemannian manifolds with Euclidean volume growth
Luigi Fontana, Carlo Morpurgo, Liuyu Qin
We obtain sharp estimates for heat kernels and Green's functions on complete noncompact Riemannian manifolds with Euclidean volume growth and nonnegative Ricci curvature. We will t…
Moser-Trudinger inequalities: from local to global
Luigi Fontana, Carlo Morpurgo, Liuyu Qin
Given a general complete Riemannian manifold , we introduce the concept of "local Moser-Trudinger inequality on ". We show how the validity of the Moser-Trudinger in…
Adams inequalities for Riesz subcritical potentials
Luigi Fontana, Carlo Morpurgo
We derive Adams inequalities for potentials on general measure spaces, extending and improving previous results obtained by the authors. The integral operators involved, which we c…
Sharp exponential integrability for critical Riesz potentials and fractional Laplacians on R^n
Luigi Fontana, Carlo Morpurgo
We derive sharp Adams inequalities for the Riesz and more general Riesz-like potentials on the whole of R^n. As a consequence, we obtain sharp Moser-Trudinger inequalities for the…
Sharp Adams and Moser-Trudinger inequalities on R^n and other spaces of infinite measure
Luigi Fontana, Carlo Morpurgo
We derive sharp Adams inequalities for the Riesz and other potentials of functions with arbitrary compact support in R^n. Up to now such results were only known for a class of func…
Self-intersections of the Riemann zeta function on the critical line
William Banks, Victor Castillo-Garate, Luigi Fontana +1
We show that the Riemann zeta function ζ has only countably many self-intersections on the critical line, i.e., for all but countably many z in C the equation ζ(1/2+it)=z has at mo…
Optimal limiting embeddings for -reduced Sobolev spaces in
Luigi Fontana, Carlo Morpurgo
We prove sharp embedding inequalities for certain reduced Sobolev spaces that arise naturally in the context of Dirichlet problems with data. We also find the optimal target…
Sharp Moser-Trudinger inequalities for the Laplacian without boundary conditions
Luigi Fontana, Carlo Morpurgo
We derive a sharp Moser-Trudinger inequality for the borderline Sobolev imbedding of W^{2,n/2}(B_n) into the exponential class, where B_n is the unit ball of R^n. The corresponding…
Adams inequalities on measure spaces
Luigi Fontana, Carlo Morpurgo
In 1988 Adams obtained sharp Moser-Trudinger inequalities on bounded domains of R^n. The main step was a sharp exponential integral inequality for convolutions with the Riesz poten…
Moser-Trudinger and Beckner-Onofri's inequalities on the CR sphere
Thomas P. Branson, Luigi Fontana, Carlo Morpurgo
We derive sharp Moser-Trudinger inequalities on the CR sphere. The first type is in the Adams form, for powers of the sublaplacian and for general spectrally defined operators on t…
-Neumann Problem in the Sobolev Topology
Luigi Fontana, Steven G. Krantz, Marco M. Peloso
We study the -Neumann problem using the Sobolev space inner product. We show that the problem can be solved on any smoothly bounded, pseudoconvex domain. We fu…
The dbar-Neumann problem in the Sobolev topology
Luigi Fontana, Steven G. Krantz, Marco M. Peloso
revision posted November 1996
Hodge theory in the Sobolev topology for the de Rham complex
Luigi Fontana, Steven G. Krantz, Marco M. Peloso
The authors study the Hodge theory of the exterior differential operator acting on -forms on a smoothly bounded domain in $\RR^{N+1}$, and on the half space $\rnp$. The nove…