S. Meda
Endpoint estimates for first-order Riesz transforms associated to the Ornstein-Uhlenbeck operator.
Mon, 02/08/2010 - 16:01 — SomNambulAuthors: G. Mauceri, S. Meda, P. Sjögren
Subjects: Functional Analysis
AbstractIn the setting of Euclidean space with the Gaussian measure g, we consider
all first-order Riesz transforms associated to the infinitesimal generator of
the Ornstein-Uhlenbeck semigroup. These operators are known to be bounded on
L^p(g), for 1<p<\infty. We determine which of them are bounded from H^1(g) to
L^1(g) and from L^\infty(g) to BMO(g). Here H^1(g) and BMO(g) are the spaces
introduced in this setting by the first two authors. Surprisingly, we find that
the results depend on the dimension of the ambient space.Atomic decomposition of Hardy type spaces on certain noncompact manifolds.
Mon, 02/08/2010 - 16:01 — SomNambulAuthors: G. Mauceri, S. Meda, M. Vallarino
Subjects: Functional Analysis
AbstractIn this paper we consider a complete connected noncompact Riemannian manifold
M with bounded geometry and spectral gap. We prove that the Hardy type spaces
X^k(M), introduced in a previous paper of the authors, have an atomic
characterization. As an application, we prove that the Riesz transforms of even
order 2k are bounded from X^k(M) to L^1(M)and on L^p(M) for 1<p<\infty.Equivalence of norms on finite linear combinations of atoms.
Thu, 10/29/2009 - 16:01 — SomNambulAuthors: G. Mauceri, S. Meda
Subjects: Functional Analysis
AbstractLet 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.
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