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Fefferman-Stein, Wainger and Sjölin proved optimal $H^{p}$ boundedness for certain oscillating multipliers on $R^{d}$ . In this article, we prove an analogue of their result on a compact Lie group.

Order convolution and vector-valued multipliers

U. B. Tewari (2007)

Colloquium Mathematicae

Let I = (0,∞) with the usual topology. For x,y ∈ I, we define xy = max(x,y). Then I becomes a locally compact commutative topological semigroup. The Banach space L¹(I) of all Lebesgue integrable functions on I becomes a commutative semisimple Banach algebra with order convolution as multiplication. A bounded linear operator T on L¹(I) is called a multiplier of L¹(I) if T(f*g) = f*Tg for all f,g ∈ L¹(I). The space of multipliers of L¹(I) was determined by Johnson and Lahr. Let X be a Banach space...

Order Isomorphisms of Fourier-Stieltjes Algebras.

Jean de Cannière, Wolfgang Arendt (1983)

Mathematische Annalen

Oscillating multipliers on noncompact symmetric spaces.

Saverio Giulini, Stefano Meda (1990)

Journal für die reine und angewandte Mathematik

Oscillating multipliers on the Heisenberg group

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

Colloquium Mathematicae

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.

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On the Fourier Transformation on Spaces of (p, q)-Multipliers.

On the Hausdorff-Young Theorem for Amalgams.

On the o-Spektrum of Regular Operators and the Spectrum of Measures.

On the Siegel-Weil Formula.

On the spectrum of the Laplacian on the affine group of the real line

Operators associated with representations of amenable groups singular integrals induced by ergodic flows, the rotation method and multipliers

Operators on VN(G) commuting with A(G)

Optimal boundedness of central oscillating multipliers on compact Lie groups

Order convolution and vector-valued multipliers

Order Isomorphisms of Fourier-Stieltjes Algebras.

Oscillating multipliers on noncompact symmetric spaces.

Oscillating multipliers on the Heisenberg group

p-Pseudomeasures and Closed Subgroups.

Recognition and limit theorems for $L_{p}$ -multipliers

Remark on Herz-Schur Multipliers on Free Groups.

Remarks on a Paper of Bachelis and Gilbert.

Resonance classes of measures.

Restrictions of Multipliers to Closed Subgroups.

Results on Banach ideals and spaces of multipliers.

Rings of regular functions on nilpotent orbits and their covers.

Currently displaying 121 – 140 of 178