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48
Endpoint Strichartz estimates
 Amer. J. Math
, 1998
"... Abstract. We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension n 4) and the Schrödinger equation (in dimension n 3). Three other applications are discussed: local existence for a nonlinear wave equation; and Stri ..."
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Cited by 266 (36 self)
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Abstract. We prove an abstract Strichartz estimate, which implies previously unknown endpoint Strichartz estimates for the wave equation (in dimension n 4) and the Schrödinger equation (in dimension n 3). Three other applications are discussed: local existence for a nonlinear wave equation; and Strichartztype estimates for more general dispersive equations and for the kinetic transport equation. 1. Introduction. In
Multilinear Calderón Zygmund theory
 ADV. IN MATH. 40
, 1996
"... A systematic treatment of multilinear CalderónZygmundoperators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, the multilinear T1 theorem, anda variety of results regarding multilinear multiplier operators. ..."
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Cited by 46 (16 self)
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A systematic treatment of multilinear CalderónZygmundoperators is presented. The theory developed includes strong type and endpoint weak type estimates, interpolation, the multilinear T1 theorem, anda variety of results regarding multilinear multiplier operators.
Weighted norm inequalities, offdiagonal estimates and elliptic operators, Part II: Offdiagonal estimates on spaces of homogeneous type
, 2005
"... Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincar ..."
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Cited by 23 (6 self)
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Abstract. This is the fourth article of our series. Here, we apply the results of [AM1] to study weighted norm inequalities for the Riesz transform of the LaplaceBeltrami operator on Riemannian manifolds and of subelliptic sum of squares on Lie groups, under the doubling volume property and Poincaré inequalities. 1. Introduction and
Planar earthmover is not in l1
 In 47th Symposium on Foundations of Computer Science (FOCS
, 2006
"... We show that any L1 embedding of the transportation cost (a.k.a. Earthmover) metric on probability measures supported on the grid {0, 1,..., n} 2 ⊆ R 2 incurs distortion Ω � � log n �. We also use Fourier analytic techniques to construct a simple L1 embedding of this space which has distortion O(lo ..."
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Cited by 12 (2 self)
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We show that any L1 embedding of the transportation cost (a.k.a. Earthmover) metric on probability measures supported on the grid {0, 1,..., n} 2 ⊆ R 2 incurs distortion Ω � � log n �. We also use Fourier analytic techniques to construct a simple L1 embedding of this space which has distortion O(log n). 1
A BeurlingHelson type theorem for modulation spaces
, 2007
"... Abstract. We prove a BeurlingHelson type theorem on modulation spaces. More precisely, we show that the only C 1 changes of variables that leave invariant the modulation spaces M p,q (R d) are affine functions on R d. A special case of our result involving the Sjöstrand algebra was considered earli ..."
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Cited by 11 (0 self)
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Abstract. We prove a BeurlingHelson type theorem on modulation spaces. More precisely, we show that the only C 1 changes of variables that leave invariant the modulation spaces M p,q (R d) are affine functions on R d. A special case of our result involving the Sjöstrand algebra was considered earlier by A. Boulkhemair. 1.
Inhomogeneous Strichartz estimates
 J. Hyperbolic Differ. Equ
"... Let (X, dµ) be a measure space, H a Hilbert space and σ> 0. Consider a family of linear operators U(t) : H → L2 X defined for each t ∈ R. Let U ∗ (t) : L2 X → H be the adjoint of U(t). We assume that the family U(t) satisfies ..."
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Cited by 10 (1 self)
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Let (X, dµ) be a measure space, H a Hilbert space and σ> 0. Consider a family of linear operators U(t) : H → L2 X defined for each t ∈ R. Let U ∗ (t) : L2 X → H be the adjoint of U(t). We assume that the family U(t) satisfies
RADIAL FOURIER MULTIPLIERS IN HIGH DIMENSIONS
"... Abstract. Given a fixed p ̸ = 2, we prove a simple and effective characterization of all radial multipliers of FL p (R d), provided that the dimension d is sufficiently large. The method also yields new L q spacetime regularity results for solutions of the wave equation in high dimensions. ..."
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Cited by 8 (8 self)
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Abstract. Given a fixed p ̸ = 2, we prove a simple and effective characterization of all radial multipliers of FL p (R d), provided that the dimension d is sufficiently large. The method also yields new L q spacetime regularity results for solutions of the wave equation in high dimensions.
Plancherel type estimates and sharp spectral multipliers
 J. FUNCT. ANAL
, 2002
"... We study general spectral multiplier theorems for selfadjoint positive definite operators on L²(X, µ), where X is any open subset of a space of homogeneous type. We show that the sharp Hörmandertype spectral multiplier theorems follow from the appropriate estimates of the L² norm of the kernel of ..."
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Cited by 7 (0 self)
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We study general spectral multiplier theorems for selfadjoint positive definite operators on L²(X, µ), where X is any open subset of a space of homogeneous type. We show that the sharp Hörmandertype spectral multiplier theorems follow from the appropriate estimates of the L² norm of the kernel of spectral multipliers and the Gaussian bounds for the corresponding heat kernel. The sharp Hörmandertype spectral multiplier theorems are motivated and connected with sharp estimates for the critical exponent for the Riesz means summability, which we also study here. We discuss several examples, which include sharp spectral multiplier theorems for a class of scattering operators on R³ and new spectral multiplier theorems for the Laguerre and Hermite expansions.
Goldstone Boson Normal Coordinates
, 2000
"... The phenomenon of spontaneous symmetry breaking is well known. It is known to be accompanied with the appearance of the `Goldstone boson'. In this paper we construct the canonical coordinates of the Goldstone boson, for quantum spin systems with short range as well as long range interactions. Keywor ..."
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Cited by 7 (4 self)
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The phenomenon of spontaneous symmetry breaking is well known. It is known to be accompanied with the appearance of the `Goldstone boson'. In this paper we construct the canonical coordinates of the Goldstone boson, for quantum spin systems with short range as well as long range interactions. Keywords Spontaneous symmetry breaking, Goldstone theorem, plasmon frequency, long wavelength limits, canonical coordinates. 1 Research Assistant of the Fund for Scientific Research  Flanders (Belgium) (F.W.O.) 1 Email: tom.michoel@fys.kuleuven.ac.be 2 Email: andre.verbeure@fys.kuleuven.ac.be Contents 1 Introduction 3 2 Canonical coordinates 8 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Normal fluctuations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.3 Reversible dynamics of fluctuations . . . . . . . . . . . . . . . . . . . . . . 12 2.4 Canonical coordinates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1...
...Estimates for functions of the LaplaceBeltrami operator on noncompact symmetric spaces, II
, 1995
"... this paper we continue the study of functional calculus for the Laplace Beltrami operator on symmetric spaces of the noncompact type begun in [3]; this paper is dedicated to a study of the Poisson semigroup, which we define shortly. Let G and K be a connected noncompact semisimple Lie group with f ..."
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Cited by 5 (3 self)
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this paper we continue the study of functional calculus for the Laplace Beltrami operator on symmetric spaces of the noncompact type begun in [3]; this paper is dedicated to a study of the Poisson semigroup, which we define shortly. Let G and K be a connected noncompact semisimple Lie group with finite center and a maximal compact subgroup thereof, and consider the symmetric space G=K; also denoted by X: We denote by n the dimension of X; by