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

Éric Ricard, Ana-Maria Stan (2011)

Colloquium Mathematicae

It is well known that in a free group , one has | | χ E | | M c b A ( ) 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 ( ) .

The space of multipliers and convolutors of Orlicz spaces on a locally compact group

Hasan P. Aghababa, Ibrahim Akbarbaglu, Saeid Maghsoudi (2013)

Studia Mathematica

Let G be a locally compact group, let (φ,ψ) be a complementary pair of Young functions, and let L φ ( G ) and L ψ ( G ) be the corresponding Orlicz spaces. Under some conditions on φ, we will show that for a Banach L φ ( G ) -submodule X of L ψ ( G ) , the multiplier space H o m L φ ( G ) ( L φ ( G ) , X * ) is a dual Banach space with predual L φ ( G ) X : = s p a n ¯ u x : u L φ ( G ) , x X , where the closure is taken in the dual space of H o m L φ ( G ) ( L φ ( G ) , X * ) . We also prove that if φ is a Δ₂-regular N-function, then C v φ ( G ) , the space of convolutors of M φ ( G ) , is identified with the dual of a Banach algebra of functions on G under pointwise...

Transferring L p multipliers

Anthony H. Dooley (1986)

Annales de l'institut Fourier

By combining some results of C. S. Herz on the Fourier algebra with the notion of contractions of Lie groups, we prove theorems which allow transference of L p multipliers either from the Lie algebra or from the Cartan motion group associated to a compact Lie group to the group itself.

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