The Herz-Schur multiplier norm of sets satisfying the Leinert condition

Éric Ricard; Ana-Maria Stan

Displaying similar documents to “The Herz-Schur multiplier norm of sets satisfying the Leinert condition”

A multiplier theorem for Fourier series in several variables

Nakhle Asmar, Florence Newberger, Saleem Watson (2006)

Colloquium Mathematicae

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We define a new type of multiplier operators on $L^{p} (^{N})$ , where $^{N}$ is the N-dimensional torus, and use tangent sequences from probability theory to prove that the operator norms of these multipliers are independent of the dimension N. Our construction is motivated by the conjugate function operator on $L^{p} (^{N})$ , to which the theorem applies as a particular example.

The Bogomolov multiplier of groups of order $p^{7}$ and exponent $p$

Zeinab Araghi Rostami, Mohsen Parvizi, Peyman Niroomand (2024)

Czechoslovak Mathematical Journal

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We conduct an in-depth investigation into the structure of the Bogomolov multiplier for groups of order $p^{7}$ $(p > 2)$ and exponent $p$ . We present a comprehensive classification of these groups, identifying those with nontrivial Bogomolov multipliers and distinguishing them from groups with trivial multipliers. Our analysis not only clarifies the conditions under which the Bogomolov multiplier is nontrivial but also refines existing computational methods, enhancing the process of...

(E,F)-Schur multipliers and applications

Fedor Sukochev, Anna Tomskova (2013)

Studia Mathematica

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For two given symmetric sequence spaces E and F we study the (E,F)-multiplier space, that is, the space of all matrices M for which the Schur product M ∗ A maps E into F boundedly whenever A does. We obtain several results asserting continuous embedding of the (E,F)-multiplier space into the classical (p,q)-multiplier space (that is, when $E = l_{p}$ , $F = l_{q}$ ). Furthermore, we present many examples of symmetric sequence spaces E and F whose projective and injective tensor products are not isomorphic...

The space of multipliers into $l_{1}$

P. Wojtaszczyk (1979)

Annales Polonici Mathematici

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Pointwise multipliers on martingale Campanato spaces

Eiichi Nakai, Gaku Sadasue (2014)

Studia Mathematica

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We introduce generalized Campanato spaces $_{p, ϕ}$ on a probability space (Ω,ℱ,P), where p ∈ [1,∞) and ϕ: (0,1] → (0,∞). If p = 1 and ϕ ≡ 1, then $_{p, ϕ} = B M O$ . We give a characterization of the set of all pointwise multipliers on $_{p, ϕ}$ .

On fixed point free involutions of $R^{1} \times S^{2}$

Gerhard X. Ritter (1976)

Colloquium Mathematicae

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Multipliers of the space $A^{p}$

I. Jovanović (1986)

Matematički Vesnik

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Completely bounded lacunary sets for compact non-abelian groups

Kathryn Hare, Parasar Mohanty (2015)

Studia Mathematica

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In this paper, we introduce and study the notion of completely bounded $Λ_{p}$ sets ( $Λ_{p}^{c b}$ for short) for compact, non-abelian groups G. We characterize $Λ_{p}^{c b}$ sets in terms of completely bounded $L^{p} (G)$ multipliers. We prove that when G is an infinite product of special unitary groups of arbitrarily large dimension, there are sets consisting of representations of unbounded degree that are $Λ_{p}$ sets for all p < ∞, but are not $Λ_{p}^{c b}$ for any p ≥ 4. This is done by showing that the space of completely bounded $L^{p} (G)$ ...

Pairs of square-free values of the type $n^{2} + 1$ , $n^{2} + 2$

Stoyan Dimitrov (2021)

Czechoslovak Mathematical Journal

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We show that there exist infinitely many consecutive square-free numbers of the form $n^{2} + 1$ , $n^{2} + 2$ . We also establish an asymptotic formula for the number of such square-free pairs when $n$ does not exceed given sufficiently large positive number.

Consecutive square-free values of the type $x^{2} + y^{2} + z^{2} + k$ , $x^{2} + y^{2} + z^{2} + k + 1$

Ya-Fang Feng (2023)

Czechoslovak Mathematical Journal

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We show that for any given integer $k$ there exist infinitely many consecutive square-free numbers of the type $x^{2} + y^{2} + z^{2} + k$ , $x^{2} + y^{2} + z^{2} + k + 1$ . We also establish an asymptotic formula for $1 \leq x, y, z \leq H$ such that $x^{2} + y^{2} + z^{2} + k$ , $x^{2} + y^{2} + z^{2} + k + 1$ are square-free. The method we used in this paper is due to Tolev.

An $M_{q} ()$ -functional calculus for power-bounded operators on certain UMD spaces

Earl Berkson, T. A. Gillespie (2005)

Studia Mathematica

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For 1 ≤ q < ∞, let $_{q} ()$ denote the Banach algebra consisting of the bounded complex-valued functions on the unit circle having uniformly bounded q-variation on the dyadic arcs. We describe a broad class ℐ of UMD spaces such that whenever X ∈ ℐ, the sequence space ℓ²(ℤ,X) admits the classes $_{q} ()$ as Fourier multipliers, for an appropriate range of values of q > 1 (the range of q depending on X). This multiplier result expands the vector-valued Marcinkiewicz Multiplier Theorem in the direction...

Oscillating multipliers on the Heisenberg group

E. K. Narayanan, S. Thangavelu (2001)

Colloquium Mathematicae

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Let ℒ be the sublaplacian on the Heisenberg group Hⁿ. A recent result of Müller and Stein shows that the operator $ℒ^{- 1 / 2} s i n \sqrt ℒ$ is bounded on $L^{p} (H ⁿ)$ for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on $L^{p}$ in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.

Variations on Bochner-Riesz multipliers in the plane

Daniele Debertol (2006)

Studia Mathematica

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We consider the multiplier $m_{μ}$ defined for ξ ∈ ℝ by $m_{μ} (ξ) ≐ {((1 - ξ ₁ ² - ξ ₂ ²) / (1 - ξ ₁))}^{μ} 1_{D} (ξ)$ , D denoting the open unit disk in ℝ. Given p ∈ ]1,∞[, we show that the optimal range of μ’s for which $m_{μ}$ is a Fourier multiplier on $L^{p}$ is the same as for Bochner-Riesz means. The key ingredient is a lemma about some modifications of Bochner-Riesz means inside convex regions with smooth boundary and non-vanishing curvature, providing a more flexible version of a result by Iosevich et al. [Publ. Mat. 46 (2002)]. As an application, we show...

The range of non-linear natural polynomials cannot be context-free

Dömötör Pálvölgyi (2020)

Kybernetika

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Suppose that some polynomial $f$ with rational coefficients takes only natural values at natural numbers, i. e., $L = {f (n) ∣ n \in ℕ} \subseteq ℕ$ . We show that the base- $q$ representation of $L$ is a context-free language if and only if $f$ is linear, answering a question of Shallit. The proof is based on a new criterion for context-freeness, which is a combination of the Interchange lemma and a generalization of the Pumping lemma.

Equalizers and coactions of groups

Martin Arkowitz, Mauricio Gutierrez (2002)

Fundamenta Mathematicae

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If f:G → H is a group homomorphism and p,q are the projections from the free product G*H onto its factors G and H respectively, let the group $_{f} \subseteq G * H$ be the equalizer of fp and q:G*H → H. Then p restricts to an epimorphism $p_{f} {= p |}_{f} :_{f} \to G$ . A right inverse (section) $G \to_{f}$ of $p_{f}$ is called a coaction on G. In this paper we study $_{f}$ and the sections of $p_{f}$ . We consider the following topics: the structure of $_{f}$ as a free product, the restrictions on G resulting from the existence of a coaction, maps of coactions and...

On $k$ -free numbers over Beatty sequences

Wei Zhang (2023)

Czechoslovak Mathematical Journal

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We consider $k$ -free numbers over Beatty sequences. New results are given. In particular, for a fixed irrational number $α > 1$ of finite type $τ < \infty$ and any constant $ε > 0$ , we can show that $\sum_{\binom{1 \leq n \leq x}{[α n + β] \in 𝒬_{k}}} 1 - \frac{x}{ζ (k)} ≪ x^{k / (2 k - 1) + ε} + x^{1 - 1 / (τ + 1) + ε},$ where $𝒬_{k}$ is the set of positive $k$ -free integers and the implied constant depends only on $α,$ $ε,$ $k$ and $β .$ This improves previous results. The main new ingredient of our idea is employing double exponential sums of the type $\sum_{1 \leq h \leq H} \sum_{\binom{1 \leq n \leq x}{n \in 𝒬_{k}}} e (ϑ h n) .$

Prescribing endomorphism algebras of $ℵ_{n}$ -free modules

Rüdiger Göbel, Daniel Herden, Saharon Shelah (2014)

Journal of the European Mathematical Society

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It is a well-known fact that modules over a commutative ring in general cannot be classified, and it is also well-known that we have to impose severe restrictions on either the ring or on the class of modules to solve this problem. One of the restrictions on the modules comes from freeness assumptions which have been intensively studied in recent decades. Two interesting, distinct but typical examples are the papers by Blass [1] and Eklof [8], both jointly with Shelah. In the first case...

Extensions of weak type multipliers

P. Mohanty, S. Madan (2003)

Studia Mathematica

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We prove that if $Λ \in M_{p} (ℝ^{N})$ and has compact support then Λ is a weak summability kernel for 1 < p < ∞, where $M_{p} (ℝ^{N})$ is the space of multipliers of $L^{p} (ℝ^{N})$ .

On the $r$ -free values of the polynomial $x^{2} + y^{2} + z^{2} + k$

Gongrui Chen, Wenxiao Wang (2023)

Czechoslovak Mathematical Journal

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Let $k$ be a fixed integer. We study the asymptotic formula of $R (H, r, k)$ , which is the number of positive integer solutions $1 \leq x, y, z \leq H$ such that the polynomial $x^{2} + y^{2} + z^{2} + k$ is $r$ -free. We obtained the asymptotic formula of $R (H, r, k)$ for all $r \geq 2$ . Our result is new even in the case $r = 2$ . We proved that $R (H, 2, k) = c_{k} H^{3} + O (H^{9 / 4 + ε})$ , where $c_{k} > 0$ is a constant depending on $k$ . This improves upon the error term $O (H^{7 / 3 + ε})$ obtained by G.-L. Zhou, Y. Ding (2022).

Operator Connes-amenability of completely bounded multiplier Banach algebras

Bahman Hayati, Abasalt Bodaghi, Massoud Amini (2019)

Archivum Mathematicum

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For a completely contractive Banach algebra $B$ , we find conditions under which the completely bounded multiplier algebra $ℳ_{c b} (B)$ is a dual Banach algebra and the operator amenability of $B$ is equivalent to the operator Connes-amenability of $ℳ_{c b} (B)$ . We also show that, in this case, these are equivalent to the existence of a normal virtual operator diagonal.