The space of multipliers into $l_1$

P. Wojtaszczyk

Displaying similar documents to “The space of multipliers into $l_{1}$ ”

Multipliers of the space $A^{p}$

I. Jovanović (1986)

Matematički Vesnik

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(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...

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 $_{p, ϕ}$ .

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

Éric Ricard, Ana-Maria Stan (2011)

Colloquium Mathematicae

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It is well known that in a free group , one has $| | χ_{E} {| |}_{M_{c b} A ()} \leq 2$ , where E is the set of all the generators. We show that the (completely) bounded multiplier norm of any set satisfying the Leinert condition depends only on its cardinality. Consequently, based on a result of Wysoczański, we obtain a formula for $| | χ_{E} {| |}_{M_{c b} A ()}$ .

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.

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 $L^{p} (ℝ^{N})$ .

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...

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.

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 $L^{p} (G)$ ...

Multilinear Fourier multipliers with minimal Sobolev regularity, I

Loukas Grafakos, Hanh Van Nguyen (2016)

Colloquium Mathematicae

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We find optimal conditions on m-linear Fourier multipliers that give rise to bounded operators from products of Hardy spaces $H^{p_{k}}$ , $0 < p_{k} \leq 1$ , to Lebesgue spaces $L^{p}$ . These conditions are expressed in terms of L²-based Sobolev spaces with sharp indices within the classes of multipliers we consider. Our results extend those obtained in the linear case (m = 1) by Calderón and Torchinsky (1977) and in the bilinear case (m = 2) by Miyachi and Tomita (2013). We also prove a coordinate-type Hörmander integral...

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...

Spaces of multipliers and their preduals for the order multiplication on [0,1]. II

Savita Bhatnagar (2004)

Colloquium Mathematicae

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Consider I = [0,1] as a compact topological semigroup with max multiplication and usual topology, and let $C (I), L^{p} (I), 1 \leq p \leq \infty$ , be the associated algebras. The aim of this paper is to study the spaces $H o m_{C (I)} (L^{r} (I), L^{p} (I))$ , r > p, and their preduals.

$L^{p}$ spectral multipliers on the free group $N_{3, 2}$

Alessio Martini, Detlef Müller (2013)

Studia Mathematica

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Let L be a homogeneous sublaplacian on the 6-dimensional free 2-step nilpotent Lie group $N_{3, 2}$ on three generators. We prove a theorem of Mikhlin-Hörmander type for the functional calculus of L, where the order of differentiability s > 6/2 is required on the multiplier.

$L^{p}$ -multipliers for the Laguerre expansions

Jolanta Dlugosz (1987)

Colloquium Mathematicae

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A characterization of the disc $D^{n}$

Th. Friedrich (1974)

Colloquium Mathematicae

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Transference and restriction of maximal multiplier operators on Hardy spaces

Zhixin Liu, Shanzhen Lu (1993)

Studia Mathematica

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The aim of this paper is to establish transference and restriction theorems for maximal operators defined by multipliers on the Hardy spaces $H^{p} (ℝ^{n})$ and $H^{p} (^{n})$ , 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an $L^{\infty} (ℝ^{n})$ function m is a maximal multiplier on $H^{p} (ℝ^{n})$ if and only if it is a maximal multiplier on $H^{p} (^{n})$ . As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered. ...