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Search Results: 1 - 10 of 1574 matches for " Frederic Bernicot "
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Local estimates and global continuities in Lebesgue spaces for bilinear operators
Frederic Bernicot
Mathematics , 2008,
Abstract: In this paper, we first prove some local estimates for bilinear operators (closely related to the bilinear Hilbert transform and similar singular operators) with truncated symbol. Such estimates, in accordance with the Heisenberg uncertainty principle correspond to a description of ``off-diagonal'' decay. In addition they allow us to prove global continuities in Lebesgue spaces for bilinear operators with spatial dependent symbol.
Maximal inequalities for dual Sobolev spaces $W^{-1,p}$ and applications to interpolation
Frederic Bernicot
Mathematics , 2008,
Abstract: We firstly describe a maximal inequality for dual Sobolev spaces W^{-1,p}. This one corresponds to a "Sobolev version" of usual properties of the Hardy-Littlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one seems to be new and we develop arguments in the general framework of Riemannian manifold. Then we present an application to obtain interpolation results for Sobolev spaces.
Multi-frequency Calderon-Zygmund analysis and connexion to Bochner-Riesz multipliers
Frederic Bernicot
Mathematics , 2012,
Abstract: In this work, we describe several results exhibited during a talk at the El Escorial 2012 conference. We aim to pursue the development of a multi-frequency Calderon-Zygmund analysis introduced in [9]. We set a definition of general multi-frequency Calderon-Zygmund operator. Unweighted estimates are obtained using the corresponding multi-frequency decomposition of [9]. Involving a new kind of maximal sharp function, weighted estimates are obtained.
Uniform estimates for paraproducts and related multilinear multipliers
Frederic Bernicot
Mathematics , 2008,
Abstract: In this paper, we prove some uniform estimates between Lebesgue and Hardy spaces for operators closely related to the multilinear paraproducts on R^d. We are looking for uniformity with respect to parameters, which allow us to disturb the geometry and the metric on $R^d$.
A bilinear pseudodifferential calculus
Frederic Bernicot
Mathematics , 2008,
Abstract: In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the bilinear Hilbert transform. We give a description of the action of our bilinear operators on Sobolev spaces. These classes also have a ``nice'' behavior through the transposition and the composition operations that we will present.
Lp estimates for non smooth bilinear Littlewood-Paley square functions on R
Frederic Bernicot
Mathematics , 2008,
Abstract: In this work, some non smooth bilinear analogues of linear Littlewood-Paley square functions on the real line are studied. These bilinear operators are closely related to the bilinear Hilbert transforms and vector valued version of these ones. Mainly we prove boundedness-properties in Lebesgue spaces for them.
A T(1)-Theorem in relation to a semigroup of operators and applications to new paraproducts
Frederic Bernicot
Mathematics , 2010,
Abstract: In this work, we are interested to develop new directions of the famous T(1)-theorem. More precisely, we develop a general framework where we look for replacing the John-Nirenberg space BMO (in the classical result) by a new BMO_{L}, associated to a semigroup of operators (e^{-tL})_{t>0}. These new spaces BMO_L (including BMO) have recently appeared in numerous works in order to extend the theory of Hardy and BMO space to more general situations. Then we give applications by describing boundedness for a new kind of paraproducts, built on the considered semigroup. In addition we obtain a version of the classical T(1) theorem for doubling Riemannian manifolds.
New Abstract Hardy Spaces
Frederic Bernicot,Jiman Zhao
Mathematics , 2007,
Abstract: The aim of this paper is to propose an abstract construction of spaces which keep the main properties of the (already known) Hardy spaces H^1. We construct spaces through an atomic (or molecular) decomposition. We prove some results about continuity from these spaces into L^1 and some results about interpolation between these spaces and the Lebesgue spaces. We also obtain some results on weighted norm inequalities. Then we apply this abstract theory to the L^p maximal regularity. Finally we present partial results in order to understand a characterization of the duals of Hardy spaces.
Abstract Hardy-Sobolev spaces and interpolation
Nadine Badr,Frederic Bernicot
Mathematics , 2009,
Abstract: The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give applications to Riesz inequalities.
Existence of sweeping process in Banach spaces under directional prox-regularity
Frederic Bernicot,Juliette Venel
Mathematics , 2008,
Abstract: This paper is devoted to weaken "classical" assumptions and give new arguments to prove existence of sweeping process (associated to the proximal normal cone of sets). Mainly we define the concept of a "directional prox-regularity" and give assumptions about a Banach space to insure the existence of such sweeping process (which permit to generalize the existing results requiring a Hilbertian structure).
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