Showing papers in "Journal of Functional Analysis in 2000"
TL;DR: In this paper, it was shown that transport inequalities, similar to the one derived by M. Talagrand (1996, Geom. Funct. Anal. 6, 587-600) for the Gaussian measure, are implied by logarithmic Sobolev inequalities.
1,080 citations
TL;DR: In this paper, the authors study the well-posedness of solutions of the heat equation with inverse-square potentials for the Cauchy-Dirichlet problem in a bounded domain and also for the cauchy problem in RN.
445 citations
TL;DR: In this article, a simple characterization of frames and Riesz families generated by shifts of a countable set of generators in terms of their behavior on subspaces of l2(Zn) was given.
283 citations
TL;DR: In this article, a spectral distribution measure for non-normal elements in a finite von Neumann algebra M with respect to a fixed normal faithful tracial state τ has been proposed, expressed explicitly in terms of the S-transform of the distribution μT*T of the positive operator T*T.
199 citations
TL;DR: In this article, a L p − L p estimate for the one-dimensional Schrodinger equation with a potential in L 1 γ where in the generic case γ > 3/2 and in the exceptional case (i.e., when there is a half-bound state of zero energy) γ ≥ 5/2 was obtained.
197 citations
TL;DR: In this article, the authors studied rearrangement-invariant quasinorms ϱR and ϱD on functions f: (0, 1) with Lebesgue measure |Ω|, and showed that for each bounded domain Ω in View the MathML sourcen, there corresponds C(|Ω |)>0 for which one has the Sobolev imbedding inequality ϱ R(u*(| Ω| t))⩽CϱD(|∇mu|* (|�
195 citations
TL;DR: In this article, a new treatment of Quiggin's and McCullough's characterization of complete Nevanlinna-pick kernels is given, and it is shown that a kernel has the matrix-valued NEP property if and only if it has the vector-valued NPN property.
190 citations
TL;DR: In this article, the super-Poincare inequality is shown to be equivalent to empty essential spectrum of the corresponding diffusion operator, provided the curvature of the diffusion operator is bounded from below.
183 citations
TL;DR: In this article, the Schrodinger operators in whole-and half-line problems were discussed and a result on the number of antibound states between any two bound states was proved.
171 citations
TL;DR: In this paper, a new derivation of upper bounds for the decay of higher order derivatives of solutions to the unforced Navier-Stokes equations in Rn is presented.
162 citations
TL;DR: In this article, a general min-max characterization of the eigenvalues in a gap of the essential spectrum of a self-adjoint unbounded operator with a Coulomb-like potential is presented.
TL;DR: In this paper, a universal blow-up pattern near the concentration point was established and the blowup energy was characterized in terms of a geometric limiting problem, which was later extended to the case of a single point blowup.
TL;DR: In this article, it was shown that the BLH Theorem of Beurling-Lax-Halmos (BLH) is invariant for multiplication by z in the Hardy space of analytic functions with values in the Hilbert space E and square summable power series.
TL;DR: In this article, the Laplace operator plus a potential on a Lipschitz domain in a Riemannian manifold with a metric tensor smooth of class C 1+ γ, for some γ > 0.
TL;DR: In this article, the authors established refinements of the classical Kato inequality for sections of a vector bundle which lie in the kernel of a natural injectively elliptic first-order linear differential operator.
TL;DR: The notion of uniformly integrable operators on L p (E, μ ) was introduced and investigated in this article, and its relation to classical compactness and hypercontractivity are exhibited.
TL;DR: In this article, a new characterization of the Daugavet property in terms of weak open sets is given, and it is shown that the operators not xing have the same property.
TL;DR: In this paper, the authors characterize finite index depth 2 inclusions of type II 1 factors in terms of actions of weak Kac algebras and weak C ∗ -Hopf algesbras.
TL;DR: In this article, the authors give a general construction which applies to any metric space equipped with a σ -finite measure and produces the desired result in all of the above cases.
TL;DR: For a class of fractals that includes the Sierpinski gasket, there is now a theory involving Laplacians, Dirichlet forms, normal derivatives, Green's functions, and the Gauss-Green integration formula, analogous to the theory of analysis on manifolds.
TL;DR: In this article, the Laplace transform realizes a topological isomorphism of the strong dual of F θ (N ) on G θ * (N) on [0, ∞+∞[.
TL;DR: In this article, Gohberg and Krupnik showed that the Riesz projection of Lp(T) on the unit circle of T is a sharp constant inequality with sharp constant, i.e., the angle between the analytic and co-analytic subspaces of T equals π/p* where p*=max (p, pp−1).
TL;DR: An expression for the L2-index of a Dirac operator coupled to a connection on a Un vector bundle over S 1×R 3 is given in this paper, where boundary conditions for the connection are given.
TL;DR: In this article, suitably weak solutions (u, p) to the Navier-Stokes equations were considered and under various assumptions on u and p, the size of the singular set was estimated.
TL;DR: In this paper, the Lp boundedness properties of a certain class of radial Fourier integral operators on a noncompact symmetric space of real rank one have been investigated, and it has been shown that if uτ is the solution at some fixed time τ of the natural wave equation on X with initial data f and g and 1
TL;DR: In this article, it was shown that Tpq = Tp∞·T∞q for tent spaces proved by R. R. Coifman et al. (1985, J. Funct. Anal.62, 304-335) holds true for all 0
TL;DR: In this article, the authors define and study a gradient on p.c.f. (post critically finite, or finitely ramified) fractals using Dirichlet (energy) form analysis developed by Kigami.
TL;DR: Amenable C*-tensor categories are realized as bimodules of finite Jones index over the AFD II 1-factor as discussed by the authors, which is the same as the one used in this paper.
TL;DR: In this paper, the authors considered the problem of finding a positive finite measure for the modified reflecting Ornstein Uhlenbeck process in an abstract Wiener space and showed that the support of the measure is concentrated in ∂Γ and the above equations reduce to the Gauss formula and the Skorohod equation.