482 research outputs found
Uniform sublevel Radon-like inequalities
This paper is concerned with establishing uniform weighted -
estimates for a class of operators generalizing both Radon-like operators and
sublevel set operators. Such estimates are shown to hold under general
circumstances whenever a scalar inequality holds for certain associated
measures (the inequality is of the sort studied by Oberlin, relating measures
of parallelepipeds to powers of their Euclidean volumes). These ideas lead to
previously unknown, weighted affine-invariant estimates for Radon-like
operators as well as new -improving estimates for degenerate Radon-like
operators with folding canonical relations which satisfy an additional
curvature condition of Greenleaf and Seeger for FIOs (building on the ideas of
Sogge and Mockenhaupt, Seeger, and Sogge); these new estimates fall outside the
range of estimates which are known to hold in the generality of the FIO
context.Comment: 40 page
Universal L^p improving for averages along polynomial curves in low dimensions
We prove sharp estimates for averaging operators along general
polynomial curves in two and three dimensions. These operators are
translation-invariant, given by convolution with the so-called affine arclength
measure of the curve and we obtain universal bounds over the class of curves
given by polynomials of bounded degree. Our method relies on a geometric
inequality for general vector polynomials together with a combinatorial
argument due to M. Christ. Almost sharp Lorentz space estimates are obtained as
well.Comment: 21 pages, with revised introduction and updated reference
On the set of L-space surgeries for links
It it known that the set of L-space surgeries on a nontrivial L-space knot is
always bounded from below. However, already for two-component torus links the
set of L-space surgeries might be unbounded from below. For algebraic
two-component links we provide three complete characterizations for the
boundedness from below: one in terms of the -function, one in terms of the
Alexander polynomial, and one in terms of the embedded resolution graph. They
show that the set of L-space surgeries is bounded from below for most algebraic
links. In fact, the used property of the -function is a sufficient condition
for non-algebraic L-space links as well.Comment: 28 pages, 13 figures; v2: Major revision, we prove a complete
characterization of algebraic links with bounded below sets of L-space
surgerie
On weak and strong solution operators for evolution equations coming from quadratic operators
International audienceWe identify, through a change of variables, solution operators for evolution equations with generators given by certain simple first-order differential operators acting on Fock spaces. This analysis applies, through unitary equivalence, to a broad class of supersymmetric quadratic multiplication-differentiation operators acting on which includes the elliptic and weakly elliptic quadratic operators. We demonstrate a variety of sharp results on boundedness, decay, and return to equilibrium for these solution operators, connecting the short-time behavior with the range of the symbol and the long-time behavior with the eigenvalues of their generators. This is particularly striking when it allows for the definition of solution operators which are compact and regularizing for large times for certain operators whose spectrum is the entire complex plane
Carleson Measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on Complex Balls
We characterize the Carleson measures for the Drury-Arveson Hardy space and
other Hilbert spaces of analytic functions of several complex variables. This
provides sharp estimates for Drury's generalization of Von Neumann's
inequality. The characterization is in terms of a geometric condition, the
"split tree condition", which reflects the nonisotropic geometry underlying the
Drury-Arveson Hardy space
Smooth perturbations of the functional calculus and applications to Riemannian geometry on spaces of metrics
We show for a certain class of operators and holomorphic functions
that the functional calculus is holomorphic. Using this result
we are able to prove that fractional Laplacians depend real
analytically on the metric in suitable Sobolev topologies. As an
application we obtain local well-posedness of the geodesic equation for
fractional Sobolev metrics on the space of all Riemannian metrics.Comment: 31 page
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