Showing papers in "Revista Matematica Iberoamericana in 1999"
TL;DR: In this article, the authors give a characterization of a parabolic Harnack inequality and Gaussian estimates for reversible Markov chains by geometric properties (volume regularity and Poincare inequality).
Abstract: On a graph, we give a characterization of a parabolic Harnack inequality and Gaussian estimates for reversible Markov chains by geometric properties (volume regularity and Poincare inequality).
324 citations
TL;DR: In this article, a sufficient condition on the kernel of T such that T is of weak type (1, 1), hence bounded on Lp(?) for 1 < p = 2; this condition is weaker then the usual Hormander integral condition.
Abstract: Let ? be a space of homogeneous type. The aims of this paper are as follows.
i) Assuming that T is a bounded linear operator on L2(?), we give a sufficient condition on the kernel of T such that T is of weak type (1,1), hence bounded on Lp(?) for 1 < p = 2; our condition is weaker then the usual Hormander integral condition.
ii) Assuming that T is a bounded linear operator on L2(O) where O is a measurable subset of ?, we give a sufficient condition on the kernel of T so that T is of weak type (1,1), hence bounded on Lp(O) for 1 < p = 2.
iii) We establish sufficient conditions for the maximal truncated operator T* which is defined by T*u(x) = supe>0 |Teu(x)|, to be Lp bounded, 1 < p < 8. Applications include weak (1,1) estimates of certain Riesz transforms, and Lp boundedness of holomorphic functional calculi of linear elliptic operators on irregular domains.
259 citations
TL;DR: In this paper, the Hardy space HA1 is defined by means of a maximal function associated with the semigroup {Tt}t>0, where Tt is a semigroup of linear operators generated by a Schrodinger operator and T is a nonnegative potential that belongs to a certain reverse Holder class.
Abstract: Let {Tt}t>0 be the semigroup of linear operators generated by a Schrodinger operator -A = ? - V, where V is a nonnegative potential that belongs to a certain reverse Holder class. We define a Hardy space HA1 by means of a maximal function associated with the semigroup {Tt}t>0. Atomic and Riesz transforms characterizations of HA1 are shown.
239 citations
TL;DR: In this paper, the authors prove global existence and uniqueness for solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which are Hdi in the i-th direction, d1 + d2 + d3 = 1 2, -1/2 < di < 1/2 and in a space which is L2 in the first two directions and B2,11/2 in third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces.
Abstract: In this paper we prove global existence and uniqueness for solutions of the 3-dimensional Navier-Stokes equations with small initial data in spaces which are Hdi in the i-th direction, d1 + d2 + d3 = 1/2, -1/2 < di < 1/2 and in a space which is L2 in the first two directions and B2,11/2 in the third direction, where H and B denote the usual homogeneous Sobolev and Besov spaces.
108 citations
TL;DR: In this paper, Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive (or a negative) constant are established.
Abstract: Several new Harnack estimates for positive solutions of the heat equation on a complete Riemannian manifold with Ricci curvature bounded below by a positive (or a negative) constant are established. These estimates are sharp both for small time, for large time and for large distance, and lead to new estimates for the heat kernel of a manifold with Ricci curvature bounded below
93 citations
TL;DR: In this paper, the authors show that the entropy dissipation associated to a function f I L 1(RN) yields a control of vf in Sobolev norms as soon as f is locally bounded below.
Abstract: We show that in the setting of the spatially homogeneous Boltzmann equation without cut-off, the entropy dissipation associated to a function f I L1(RN) yields a control of vf in Sobolev norms as soon as f is locally bounded below. Under this additional assumption of lower bound, our result is an improvement of a recent estimate given by P.-L. Lions, and is optimal in a certain sense.
68 citations
TL;DR: In this paper, the sub-Laplacian on the Heisenberg group Hm was shown to extend to a bounded operator on Lp(Hm), for 1 = p = 8, when a > (d - 1) |1/p - 1/2|.
Abstract: Let £ denote the sub-Laplacian on the Heisenberg group Hm. We prove that eiv£ / (1 - £)a/2 extends to a bounded operator on Lp(Hm), for 1 = p = 8, when a > (d - 1) |1/p - 1/2|.
45 citations
TL;DR: In this paper, a class of non-separable QMF's for L2(R2) of arbitrarily high regularity was constructed. But these QMF classes are not separable.
Abstract: By means of simple computations, we construct new classes of non separable QMF's. Some of these QMF's will lead to non separable dyadic compactly supported orthonormal wavelet bases for L2(R2) of arbitrarily high regularity.
37 citations
TL;DR: In this paper, the authors show how well-known results from the theory of (regular) elliptic boundary value problems, function spaces and interpolation, subordination in the sense of Bochner and Dirichlet forms can be combined and how one can thus get some new aspects in each of these fields.
Abstract: In this paper we want to show how well-known results from the theory of (regular) elliptic boundary value problems, function spaces and interpolation, subordination in the sense of Bochner and Dirichlet forms can be combined and how one can thus get some new aspects in each of these fields.
36 citations
TL;DR: In this article, the hyperbolic isoperimetric inequality of Riemannian manifold S is defined, and it is shown that for every relatively compact domain an open and connected set G with smooth boundary one has that.
Abstract: ds jdzj jzj With this metric S is a complete Riemannian manifold with constant curvature The only Riemann surfaces which are left out are the sphere the plane the punctured plane and the tori It is convenient to remark that this de nition of hyperbolic Rie mann surface is not universally accepted since sometimes the word hyperbolic refers to the existence of Green s function We say that S satis es the hyperbolic isoperimetric inequality HII if S is a hyperbolic Riemann surface and there exists a constant h such that for every relatively compact domain an open and connected set G with smooth boundary one has that
31 citations
TL;DR: In this article, the authors show how certain geometric conditions on a planar set imply that the set must lie on a quasicircle, and give a geometric characterization of all subsets of the plane that are quasiconformally equivalent to the usual Cantor middle-third set.
Abstract: We show how certain geometric conditions on a planar set imply that the set must lie on a quasicircle, and we give a geometric characterization of all subsets of the plane that are quasiconformally equivalent to the usual Cantor middle-third set.
TL;DR: In this article, the authors established a Lieb-Thirring type estimate for Pauli Hamiltomans with non-homogeneous magnetic fields and applied the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.
Abstract: We establish a Lieb-Thirring type estimate for Pauli Hamiltomans with non-homogeneous magnetic fields. Besides of depending on the size of the field, the bound also takes into account the size of the field gradient. We then apply the inequality to prove stability of non-relativistic quantum mechanical matter coupled to the quantized ultraviolet-cutoff electromagnetic field for arbitrary values of the fine structure constant.
TL;DR: The extremal dilatation problem for quasiconformal homeomorphisms of D was studied in this paper, where it was shown that if f is analytic, univalent and area-integrable on D, and f(0) = 0 then it is possible to dilate f to 0.
Abstract: Let D = {z: |z| 0 we define Se = {z: |arg z| 0 there exists a d > 0 such that if f is analytic, univalent and area-integrable on D, and f(0) = 0 then
This problem arose in connection with a characterization by Hamilton, Reich and Strebel of extremal dilatation for quasiconformal homeomorphisms of D.
TL;DR: In this article, the authors considered the controllability and observation problem for a simple model describing the interaction between a fluid and a beam, and showed that analytic functions can be controlled within finite time.
Abstract: We consider the controllability and observation problem for a simple model describing the interaction between a fluid and a beam. For this model, microlocal propagation of singularities proves that the space of controlled functions is smaller that the energy space. We use spectral properties and an explicit construction of biorthogonal sequences to show that analytic functions can be controlled within finite time. We also give an estimate for this time, related to the amount of analyticity of the latter function.
TL;DR: In this article, it was shown that an outer function with BMO modulus need not belong to BMOA and some related results for the Bloch space were obtained for the same problem.
Abstract: . The paper contains a complete characterization of the moduli of BMOA functions. These are described explicitly by a certain Muckenhoupt-type condition involving Poisson integrals. As a consequence, it is shown that an outer function with BMO modulus need not belong to BMOA. Some related results are obtained for the Bloch space.
TL;DR: In this article, the authors consider the semi-direct product of R*+ and Rd, d = 1 and consider the product group Gd,N = Gd x RN, N = 1.
Abstract: Let Gd be the semi-direct product of R*+ and Rd, d = 1 and let us consider the product group Gd,N = Gd x RN, N = 1. For a large class of probability measures µ on Gd,N, one prove that there exists ?(µ) I ]0,1] such that the sequence of finite measures
{(n(N+3)/2 / ?(µ)n) µ*n}n = 1
converges weakly to a non-degenerate measure.
TL;DR: In this article, the authors define a new numerical invariant of valuations centered in a regular two-dimensional regular local ring, which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation.
Abstract: . The purpose of this paper is to define a new numerical invariant of valuations centered in-a regular two-dimensional regular local ring. For this, we define a sequence of non-negative rational numbers delta v = [delta v,(j)] sub j>-0 which is determined by the proximity relations of the successive quadratic transformations at the points determined by a valuation v. This sequence is characterized by seven combinatorial properties, so that any sequence of non-negative rational numbers having the above properties is the sequence associated to a valuation.
Journal Article•
TL;DR: Balanced Bloch functions as mentioned in this paper generalize the theorem of Rohde that, for every "bad" Bloch function, g(r dseta) (r --- 1) follows any prescribed curve at a bounded distance in a set of Hausdorff dimension almost one.
Abstract: A Bloch function g is a function analytic in the unit disk such that (1 - / z / elevado a 2) g' (z) / is bounded. First we generalize the theorem of Rohde that, for every "bad" Bloch function, g(r dseta) (r --- 1) follows any prescribed curve at a bounded distance for dseta in a set of Hausdorff dimension almost one. Then we introduce balanced Bloch functions. They are characterized by the fact that g'(z) / does not vary much on each circle [ / z / = r] except for small exceptional arcs. We show e.g. that.
Abstract: We prove nearly sharp Orlicz space estimates for maximal averages over flat radial hypersurfaces in ${\Bbb R}^d$, $d \ge 3$.