49 research outputs found
Multi-frequency Calderon-Zygmund analysis and connexion to Bochner-Riesz multipliers
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.Comment: 13 page
Boundedness of smooth bilinear square functions and applications to some bilinear pseudo-differential operators
This paper is devoted to the proof of boundedness of bilinear smooth square
functions. Moreover, we deduce boundedness of some bilinear pseudo-differential
operators associated with symbols belonging to a subclass of .Comment: 27 page
New Abstract Hardy Spaces
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.Comment: 53 page
Bilinear dispersive estimates via space-time resonances, part II: dimensions 2 and 3
Consider a bilinear interaction between two linear dispersive waves with a
generic resonant structure (roughly speaking, space and time resonant sets
intersect transversally). We derive an asymptotic equivalent of the solution
for data in the Schwartz class, and bilinear dispersive estimates for data in
weighted Lebesgue spaces. An application to water waves with infinite depth,
gravity and surface tension is also presented.Comment: 45 page
Bilinear oscillatory integrals and boundedness for new bilinear multipliers
We consider bilinear oscillatory integrals, i.e. pseudo-product operators
whose symbol involves an oscillating factor. Lebesgue space inequalities are
established, which give decay as the oscillation becomes stronger ; this
extends the well-known linear theory of oscillatory integral in some
directions. The proof relies on a combination of time-frequency analysis of
Coifman-Meyer type with stationary and non-stationary phase estimates. As a
consequence of this analysis, we obtain Lebesgue estimates for new bilinear
multipliers defined by non-smooth symbols.Comment: 35 pages, 3 figure
Existence of solutions for second-order differential inclusions involving proximal normal cones
In this work, we prove global existence of solutions for second order
differential problems in a general framework. More precisely, we consider
second order differential inclusions involving proximal normal cone to a
set-valued map. This set-valued map is supposed to take admissible values (so
in particular uniformly prox-regular values, which may be non-smooth and
non-convex). Moreover we require the solution to satisfy an impact law,
appearing in the description of mechanical systems with inelastic shocks.Comment: 37 page