The space of multipliers into
P. Wojtaszczyk (1979)
Annales Polonici Mathematici
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P. Wojtaszczyk (1979)
Annales Polonici Mathematici
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I. Jovanović (1986)
Matematički Vesnik
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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 , ). Furthermore, we present many examples of symmetric sequence spaces E and F whose projective and injective tensor products are not isomorphic...
E. K. Narayanan (2003)
Colloquium Mathematicae
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We study boundedness of certain multiplier transforms associated to the special Hermite operator.
Jolanta Dlugosz (1987)
Colloquium Mathematicae
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Jongchon Kim (2015)
Studia Mathematica
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We prove endpoint bounds for the square function associated with radial Fourier multipliers acting on radial functions. This is a consequence of endpoint bounds for a corresponding square function for Hankel multipliers. We obtain a sharp Marcinkiewicz-type multiplier theorem for multivariate Hankel multipliers and bounds of maximal operators generated by Hankel multipliers as corollaries. The proof is built on techniques developed by Garrigós and Seeger for characterizations of...
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 , , to Lebesgue spaces . 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...
Éric Ricard, Ana-Maria Stan (2011)
Colloquium Mathematicae
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It is well known that in a free group , one has , 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 .
Gilles Pisier (2001)
Colloquium Mathematicae
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We study the space of functions φ: ℕ → ℂ such that there is a Hilbert space H, a power bounded operator T in B(H) and vectors ξ, η in H such that φ(n) = ⟨Tⁿξ,η⟩. This implies that the matrix is a Schur multiplier of B(ℓ₂) or equivalently is in the space (ℓ₁ ⊗̌ ℓ₁)*. We show that the converse does not hold, which answers a question raised by Peller [Pe]. Our approach makes use of a new class of Fourier multipliers of H¹ which we call “shift-bounded”. We show that there is a φ which...
Nakhle Asmar, Florence Newberger, Saleem Watson (2006)
Colloquium Mathematicae
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We define a new type of multiplier operators on , where 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 , to which the theorem applies as a particular example.
Eiichi Nakai, Gaku Sadasue (2014)
Studia Mathematica
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We introduce generalized Campanato spaces on a probability space (Ω,ℱ,P), where p ∈ [1,∞) and ϕ: (0,1] → (0,∞). If p = 1 and ϕ ≡ 1, then . We give a characterization of the set of all pointwise multipliers on .
P. Mohanty, S. Madan (2003)
Studia Mathematica
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We prove that if and has compact support then Λ is a weak summability kernel for 1 < p < ∞, where is the space of multipliers of .
Cédric Arhancet (2012)
Colloquium Mathematicae
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Let G be an infinite locally compact abelian group and X be a Banach space. We show that if every bounded Fourier multiplier T on L²(G) has the property that is bounded on L²(G,X) then X is isomorphic to a Hilbert space. Moreover, we prove that if 1 < p < ∞, p ≠ 2, then there exists a bounded Fourier multiplier on which is not completely bounded. Finally, we examine unconditionality from the point of view of Schur multipliers. More precisely, we give several necessary and sufficient...
Daniele Debertol (2006)
Studia Mathematica
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We consider the multiplier defined for ξ ∈ ℝ by , D denoting the open unit disk in ℝ. Given p ∈ ]1,∞[, we show that the optimal range of μ’s for which is a Fourier multiplier on 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...
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 is bounded on for all p satisfying |1/p - 1/2| < 1/(2n). In this paper we show that the same operator is bounded on in the bigger range |1/p - 1/2| < 1/(2n-1) if we consider only functions which are band limited in the central variable.
Loukas Grafakos, Nigel J. Kalton (2001)
Studia Mathematica
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This article is concerned with the question of whether Marcinkiewicz multipliers on give rise to bilinear multipliers on ℝⁿ × ℝⁿ. We show that this is not always the case. Moreover, we find necessary and sufficient conditions for such bilinear multipliers to be bounded. These conditions in particular imply that a slight logarithmic modification of the Marcinkiewicz condition gives multipliers for which the corresponding bilinear operators are bounded on products of Lebesgue and Hardy...
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 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.
Michał Lorens (1980)
Annales Polonici Mathematici
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Tadeusz Pytlik (1984)
Colloquium Mathematicae
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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 and , 0 < p ≤ 1, which generalize the results of Kenig-Tomas for the case p > 1. We prove that under a mild regulation condition, an function m is a maximal multiplier on if and only if it is a maximal multiplier on . As an application, the restriction of maximal multipliers to lower dimensional Hardy spaces is considered. ...
Earl Berkson, T. A. Gillespie (2005)
Studia Mathematica
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For 1 ≤ q < ∞, let 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 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...
Antonio Cordoba, B. Lopez-Melero (1981)
Annales de l'institut Fourier
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Writing . E. Stein conjectured for , and . We prove this conjecture. We prove also a.e. We only assume .
Kathryn Hare, Parasar Mohanty (2015)
Studia Mathematica
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In this paper, we introduce and study the notion of completely bounded sets ( for short) for compact, non-abelian groups G. We characterize sets in terms of completely bounded 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 sets for all p < ∞, but are not for any p ≥ 4. This is done by showing that the space of completely bounded ...
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 , be the associated algebras. The aim of this paper is to study the spaces , r > p, and their preduals.
Shangquan Bu (2013)
Studia Mathematica
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Using known results on operator-valued Fourier multipliers on vector-valued function spaces, we give necessary or sufficient conditions for the well-posedness of the second order degenerate equations (P₂): d/dt (Mu’)(t) = Au(t) + f(t) (0 ≤ t ≤ 2π) with periodic boundary conditions u(0) = u(2π), (Mu’)(0) = (Mu’)(2π), in Lebesgue-Bochner spaces , periodic Besov spaces and periodic Triebel-Lizorkin spaces , where A and M are closed operators in a Banach space X satisfying D(A) ⊂ D(M)....
Epperson Jay, Frazier Michael
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Abstract We develop an almost orthogonal wavelet-type expansion in ℝ² which is adapted to polar coordinates. We start by defining a product Fourier-Hankel transform f̂ and proving a sampling formula for f such that f̂ is compactly supported. For general f, the sampling formula and a partition of unity lead to an identity of the form , in which each function and is concentrated near a certain annular sector, has compactly supported product Fourier-Hankel transform, and is smooth...
F. M. Ragab (1963)
Annales Polonici Mathematici
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Savita Bhatnagar, H. L. Vasudeva (2002)
Colloquium Mathematicae
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Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I), , 1 ≤ p ≤ ∞, are the associated Banach algebras. The aim of the paper is to characterise and their preduals.
S. Thangavelu (2002)
Colloquium Mathematicae
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Let G be a semisimple Lie group with Iwasawa decomposition G = KAN. Let X = G/K be the associated symmetric space and assume that X is of rank one. Let M be the centraliser of A in K and consider an orthonormal basis of L²(K/M) consisting of K-finite functions of type δ on K/M. For a function f on X let f̃(λ,b), λ ∈ ℂ, be the Helgason Fourier transform. Let be the heat kernel associated to the Laplace-Beltrami operator and let be the Kostant polynomials. We establish the following...