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An L p -version of a theorem of D.A. Raikov

Gero Fendler (1985)

Annales de l'institut Fourier

Let G be a locally compact group, for p ( 1 , ) 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.

An Lp − Lq - Version of Morgan's Theorem Associated with Partial Differential Operators

Kamoun, Lotfi (2005)

Fractional Calculus and Applied Analysis

2000 Mathematics Subject Classification: 42B10, 43A32.In this paper we take the strip KL = [0, +∞[×[−Lπ, Lπ], where L is a positive integer. We consider, for a nonnegative real number α, two partial differential operators D and Dα on ]0, +∞[×] − Lπ, Lπ[. We associate a generalized Fourier transform Fα to the operators D and Dα. For this transform Fα, we establish an Lp − Lq − version of the Morgan's theorem under the assumption 1 ≤ p, q ≤ +∞.

An obstruction to p -dimension

Nicolas Monod, Henrik Densing Petersen (2014)

Annales de l’institut Fourier

Let G be any group containing an infinite elementary amenable subgroup and let 2 < p < . We construct an exhaustion of p G by closed invariant subspaces which all intersect trivially a fixed non-trivial closed invariant subspace. This is an obstacle to p -dimension and gives an answer to a question of Gaboriau.

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