Multipliers of Hankel transformable generalized functions

Jorge J. Betancor; Isabel Marrero

Displaying similar documents to “Multipliers of Hankel transformable generalized functions”

Endpoint bounds of square functions associated with Hankel multipliers

Jongchon Kim (2015)

Studia Mathematica

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We prove endpoint bounds for the square function associated with radial Fourier multipliers acting on $L^{p}$ 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 $L^{p}$ bounds of maximal operators generated by Hankel multipliers as corollaries. The proof is built on techniques developed by Garrigós and Seeger for characterizations of...

An $L^{p}$ -version of a theorem of D.A. Raikov

Gero Fendler (1985)

Annales de l'institut Fourier

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Let $G$ be a locally compact group, for $p \in (1, \infty)$ let $P f_{p} (G)$ denote the closure of $L^{1} (G)$ in the convolution operators on $L^{p} (G)$ . Denote $W_{p} (G)$ the dual of $P f_{p} (G)$ which is contained in the space of pointwise multipliers of the Figa-Talamanca Herz space $A_{p} (G)$ . It is shown that on the unit sphere of $W_{p} (G)$ the $σ (W_{p}, P f_{p})$ topology and the strong $A_{p}$ -multiplier topology coincide.

Symmetric Bessel multipliers

Khadija Houissa, Mohamed Sifi (2012)

Colloquium Mathematicae

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We study the $L^{p}$ -boundedness of linear and bilinear multipliers for the symmetric Bessel transform.

Multipliers of the Hardy space H¹ and power bounded operators

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 ${(φ (i + j))}_{i, j \geq 0}$ 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...

The space of multipliers into $l_{1}$

P. Wojtaszczyk (1979)

Annales Polonici Mathematici

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The Marcinkiewicz multiplier condition for bilinear operators

Loukas Grafakos, Nigel J. Kalton (2001)

Studia Mathematica

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This article is concerned with the question of whether Marcinkiewicz multipliers on $ℝ^{2 n}$ 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...

Unconditionality, Fourier multipliers and Schur multipliers

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 $T \otimes I d_{X}$ 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 $L^{p} (G)$ 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...

Multipliers for the twisted Laplacian

E. K. Narayanan (2003)

Colloquium Mathematicae

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We study $¹ - L^{p}$ boundedness of certain multiplier transforms associated to the special Hermite operator.

Multipliers of the space $A^{p}$

I. Jovanović (1986)

Matematički Vesnik

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Unitary multipliers on $L_{2} (G)$

Tadeusz Pytlik (1984)

Colloquium Mathematicae

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Topological classification of strong duals to nuclear (LF)-spaces

Taras Banakh (2000)

Studia Mathematica

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We show that the strong dual X’ to an infinite-dimensional nuclear (LF)-space is homeomorphic to one of the spaces: $ℝ^{ω}$ , $ℝ^{\infty}$ , $Q \times ℝ^{\infty}$ , $ℝ^{ω} \times ℝ^{\infty}$ , or ${(ℝ^{\infty})}^{ω}$ , where $ℝ^{\infty} = l i m ℝ^{n}$ and $Q = {[- 1, 1]}^{ω}$ . In particular, the Schwartz space D’ of distributions is homeomorphic to ${(ℝ^{\infty})}^{ω}$ . As a by-product of the proof we deduce that each infinite-dimensional locally convex space which is a direct limit of metrizable compacta is homeomorphic either to $ℝ^{\infty}$ or to $Q \times ℝ^{\infty}$ . In particular, the strong dual to any metrizable infinite-dimensional Montel space is homeomorphic...

Strong topologies on vector-valued function spaces

Marian Nowak (2000)

Czechoslovak Mathematical Journal

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Let $(X, ∥ \cdot ∥_{X})$ be a real Banach space and let $E$ be an ideal of $L^{0}$ over a $σ$ -finite measure space $(Ø, Σ, μ)$ . Let $(X)$ be the space of all strongly $Σ$ -measurable functions $f Ø \to X$ such that the scalar function $\tilde{f}$ , defined by $\tilde{f} (ø) = {∥ f (ø) ∥}_{X}$ for $ø \in Ø$ , belongs to $E$ . The paper deals with strong topologies on $E (X)$ . In particular, the strong topology $β (E (X), E {(X)}_{n}^{\sim})$ ( $E {(X)}_{n}^{\sim} =$ the order continuous dual of $E (X)$ ) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies.