988 research outputs found
Riesz Transforms and Spectral Multipliers of the Hodge-Laguerre Operator
On , endowed with the Laguerre probability measure
, we define a Hodge-Laguerre operator
acting on differential
forms. Here is the Laguerre exterior differentiation operator, defined
as the classical exterior differential, except that the partial derivatives
are replaced by the "Laguerre derivatives"
, and is the adjoint of with
respect to inner product on forms defined by the Euclidean structure and the
Laguerre measure . We prove dimension-free bounds on ,
, for the Riesz transforms and
. As applications we prove the strong
Hodge-de Rahm-Kodaira decomposition for forms in and deduce existence and
regularity results for the solutions of the Hodge and de Rham equations in
. We also prove that for suitable functions the operator
is bounded on , .Comment: 49 page
Equivalence of norms on finite linear combinations of atoms
Let M be a space of homogeneous type and denote by F^\infty_{cont}(M) the
space of finite linear combinations of continuous (1,\infty)-atoms. In this
note we give a simple function theoretic proof of the equivalence on
F^\infty_{cont}(M) of the H^1-norm and the norm defined in terms of finite
linear combinations of atoms. The result holds also for the class of
nondoubling metric measure spaces considered in previous works of A. Carbonaro
and the authors.Comment: 10 pages, revised argumen
Higher order Riesz transforms on noncompact symmetric spaces
In this note we prove various sharp boundedness results on suitable Hardy
type spaces for Riesz transforms of arbitrary order on noncompact symmetric
spaces of arbitrary rank.Comment: v2: the first version has been revised and splitted up in two papers,
of which this new version is one par
Estimates for functions of the Laplacian on manifolds with bounded geometry
In this paper we consider a complete connected noncompact Riemannian manifold
M with Ricci curvature bounded from below and positive injectivity radius.
Denote by L the Laplace-Beltrami operator on M. We assume that the kernel
associated to the heat semigroup generated by L satisfies a mild decay
condition at infinity. We prove that if m is a bounded holomorphic function in
a suitable strip of the complex plane, and satisfies Mihlin-Hormander type
conditions of appropriate order at infinity, then the operator m(L) extends to
an operator of weak type 1.
This partially extends a celebrated result of J. Cheeger, M. Gromov and M.
Taylor, who proved similar results under much stronger curvature assumptions on
M, but without any assumption on the decay of the heat kernel.Comment: 19 page
La straniera di Younis Tawfik: un dialogo tra due culture
In 1999 the Iraqi migrant writer Younis Tawfik was awarded several literary prizes for his novel La straniera, written in Italian and published by Bompiani. In this essay I will discuss some aspects of the novel that might have contribuited to its success. After a short presentation of the author and of the content of the novel, I will analyse La straniera, in order to show the novelty of its structure. Furthermore, I will expalin how this hybrid work reveals the double culture of the author from a literary and linguistic point of view. I will also consider how the author contributed to the current debate on migration, by examining his treatment of some themes related to this phenomenon
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