Littlewood-Paley decompositions on manifolds with ends

Jean-Marc Bouclet

Displaying similar documents to “Littlewood-Paley decompositions on manifolds with ends”

Riemannian regular $σ$ -manifolds

A. A. Ermolitski (1994)

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The ℤ₂-cohomology cup-length of real flag manifolds

Július Korbaš, Juraj Lörinc (2003)

Fundamenta Mathematicae

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Using fiberings, we determine the cup-length and the Lyusternik-Shnirel’man category for some infinite families of real flag manifolds $O (n ₁ + . . . + n_{q}) / O (n ₁) \times . . . \times O (n_{q})$ , q ≥ 3. We also give, or describe ways to obtain, interesting estimates for the cup-length of any $O (n ₁ + . . . + n_{q}) / O (n ₁) \times . . . \times O (n_{q})$ , q ≥ 3. To present another approach (combining well with the “method of fiberings”), we generalize to the real flag manifolds Stong’s approach used for calculations in the ℤ₂-cohomology algebra of the Grassmann manifolds.

The systolic constant of orientable Bieberbach 3-manifolds

Chady El Mir, Jacques Lafontaine (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

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A compact manifold is called if it carries a flat Riemannian metric. Bieberbach manifolds are aspherical, therefore the supremum of their systolic ratio, over the set of Riemannian metrics, is finite by a fundamental result of M. Gromov. We study the optimal systolic ratio of compact $3$ -dimensional orientable Bieberbach manifolds which are not tori, and prove that it cannot be realized by a flat metric. We also highlight a metric that we construct on one type of such manifolds ( $C_{2}$ ) which...

Pseudosymmetric and Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds

N. Malekzadeh, E. Abedi, U.C. De (2016)

Archivum Mathematicum

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In this paper we classify pseudosymmetric and Ricci-pseudosymmetric $(κ, μ)$ -contact metric manifolds in the sense of Deszcz. Next we characterize Weyl-pseudosymmetric $(κ, μ)$ -contact metric manifolds.

Holonomy groups of complete flat manifolds

Michał Sadowski (2007)

Banach Center Publications

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We present short direct proofs of two known properties of complete flat manifolds. They say that the diffeomorphism classes of m-dimensional complete flat manifolds form a finite set $S_{C F} (m)$ and that each element of $S_{C F} (m)$ is represented by a manifold with finite holonomy group.

Admissibly integral manifolds for semilinear evolution equations

Nguyen Thieu Huy, Vu Thi Ngoc Ha (2014)

Annales Polonici Mathematici

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We prove the existence of integral (stable, unstable, center) manifolds of admissible classes for the solutions to the semilinear integral equation $u (t) = U (t, s) u (s) + \int_{s}^{t} U (t, ξ) f (ξ, u (ξ)) d ξ$ when the evolution family ${(U (t, s))}_{t \geq s}$ has an exponential trichotomy on a half-line or on the whole line, and the nonlinear forcing term f satisfies the (local or global) φ-Lipschitz conditions, i.e., ||f(t,x)-f(t,y)|| ≤ φ(t)||x-y|| where φ(t) belongs to some classes of admissible function spaces. These manifolds are formed by trajectories of the...

Global integral formulas for solving the $\bar{\partial}$ -equation on Stein manifolds

Gennadi M. Henkin, Jürgen Leiterer (1981)

Annales Polonici Mathematici

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The maximal theorem for weighted grand Lebesgue spaces

Alberto Fiorenza, Babita Gupta, Pankaj Jain (2008)

Studia Mathematica

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We study the Hardy inequality and derive the maximal theorem of Hardy and Littlewood in the context of grand Lebesgue spaces, considered when the underlying measure space is the interval (0,1) ⊂ ℝ, and the maximal function is localized in (0,1). Moreover, we prove that the inequality ${| | M f | |}_{p), w} {\leq c | | f | |}_{p), w}$ holds with some c independent of f iff w belongs to the well known Muckenhoupt class $A_{p}$ , and therefore iff ${| | M f | |}_{p, w} {\leq c | | f | |}_{p, w}$ for some c independent of f. Some results of similar type are discussed for the case of small...

Geometry of manifolds which admit conservation laws

David E. Blair, Alexander P. Stone (1971)

Annales de l'institut Fourier

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Let $M$ be an $(n + 1)$ -dimensional Riemannian manifold admitting a covariant constant endomorphism $h$ of the localized module of 1-forms with distinct non-zero eigenvalues. After it is shown that $M$ is locally flat, a manifold $N$ immersed in $M$ is studied. The manifold $N$ has an induced structure with $n$ of the same eigenvalues if and only if the normal to $N$ is a fixed direction of $h$ . Finally conditions under which $N$ is invariant under $h$ , $N$ is totally geodesic and the induced structure has vanishing...

An inclusion operator in Hardy spaces on the unit ball in $C^{N}$

M. Jevtić (1988)

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How to define "convex functions" on differentiable manifolds

Stefan Rolewicz (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In the paper a class of families (M) of functions defined on differentiable manifolds M with the following properties: $1_{}$ . if M is a linear manifold, then (M) contains convex functions, $2_{}$ . (·) is invariant under diffeomorphisms, $3_{}$ . each f ∈ (M) is differentiable on a dense $G_{δ}$ -set, is investigated.

On weighted Hardy spaces on the unit disk

Evgeny A. Poletsky, Khim R. Shrestha (2015)

Banach Center Publications

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In this paper we completely characterize those weighted Hardy spaces that are Poletsky-Stessin Hardy spaces $H_{u}^{p}$ . We also provide a reduction of $H^{\infty}$ problems to $H_{u}^{p}$ problems and demonstrate how such a reduction can be used to make shortcuts in the proofs of the interpolation theorem and corona problem.

Homotopy invariance of higher signatures and $3$ -manifold groups

Michel Matthey, Hervé Oyono-Oyono, Wolfgang Pitsch (2008)

Bulletin de la Société Mathématique de France

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For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable $3$ -manifolds, including the “piecewise geometric” ones in the sense of Thurston. In particular, this class, that will be carefully described, is the class of all orientable $3$ -manifolds if the Thurston Geometrization Conjecture is true. In fact, for this type of groups, we show that the Baum-Connes Conjecture With Coefficients...

Essential norms of weighted composition operators between Hardy spaces $H^{p}$ and $H^{q}$ for 1 ≤ p,q ≤ ∞

R. Demazeux (2011)

Studia Mathematica

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We complete the different cases remaining in the estimation of the essential norm of a weighted composition operator acting between the Hardy spaces $H^{p}$ and $H^{q}$ for 1 ≤ p,q ≤ ∞. In particular we give some estimates for the cases 1 = p ≤ q ≤ ∞ and 1 ≤ q < p ≤ ∞.

Weighted variable $L^{p}$ integral inequalities for the maximal operator on non-increasing functions

C. J. Neugebauer (2009)

Studia Mathematica

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Let $B_{p}$ be the Ariõ-Muckenhoupt weight class which controls the weighted $L^{p}$ -norm inequalities for the Hardy operator on non-increasing functions. We replace the constant p by a function p(x) and examine the associated $L^{p (x)}$ -norm inequalities of the Hardy operator.

H¹ and BMO for certain locally doubling metric measure spaces of finite measure

Andrea Carbonaro, Giancarlo Mauceri, Stefano Meda (2010)

Colloquium Mathematicae

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In a previous paper the authors developed an H¹-BMO theory for unbounded metric measure spaces (M,ρ,μ) of infinite measure that are locally doubling and satisfy two geometric properties, called “approximate midpoint” property and “isoperimetric” property. In this paper we develop a similar theory for spaces of finite measure. We prove that all the results that hold in the infinite measure case have their counterparts in the finite measure case. Finally, we show that the theory applies...

On the principle of real moduli flexibility: perfect parametrizations

Edoardo Ballico, Riccardo Ghiloni (2014)

Annales Polonici Mathematici

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Let V be a real algebraic manifold of positive dimension. The aim of this paper is to show that, for every integer b (arbitrarily large), there exists a trivial Nash family $= {V_{y}}_{y \in R^{b}}$ of real algebraic manifolds such that V₀ = V, is an algebraic family of real algebraic manifolds over $y \in R^{b} ∖ 0$ (possibly singular over y = 0) and is perfectly parametrized by $R^{b}$ in the sense that $V_{y}$ is birationally nonisomorphic to $V_{z}$ for every $y, z \in R^{b}$ with y ≠ z. A similar result continues to hold if V is a singular real algebraic...

The Hausdorff operators on the real Hardy spaces $H^{p} (ℝ)$

Yuichi Kanjin (2001)

Studia Mathematica

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We prove that the Hausdorff operator generated by a function ϕ is bounded on the real Hardy space $H^{p} (ℝ)$ , 0 < p ≤ 1, if the Fourier transform ϕ̂ of ϕ satisfies certain smoothness conditions. As a special case, we obtain the boundedness of the Cesàro operator of order α on $H^{p} (ℝ)$ , 2/(2α+1) < p ≤ 1. Our proof is based on the atomic decomposition and molecular characterization of $H^{p} (ℝ)$ .

On $2p$ -dimensional Riemannian manifolds with positive scalar curvature

Domenico Perrone (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

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In questo lavoro si danno alcuni risultati sugli spettri degli operatori di Laplace per varietà Riemanniane compatte con curvatura scalare positiva e di dimensione $2p$ . Ad essi si aggiunge una osservazione riguardante la congettura di Yamabe.