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L p spectral multipliers on the free group N 3 , 2

Alessio Martini, Detlef Müller (2013)

Studia Mathematica

Let L be a homogeneous sublaplacian on the 6-dimensional free 2-step nilpotent Lie group N 3 , 2 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.

Locally convex algebras which determine a locally compact group

Gholam Hossein Esslamzadeh, Hossein Javanshiri, Rasoul Nasr-Isfahani (2016)

Studia Mathematica

There are several algebras associated with a locally compact group 𝓖 which determine 𝓖 in the category of topological groups, such as L¹(𝓖), M(𝓖), and their second duals. In this article we add a fairly large family of locally convex algebras to this list. More precisely, we show that for two infinite locally compact groups 𝓖₁ and 𝓖₂, there are infinitely many locally convex topologies τ₁ and τ₂ on the measure algebras M(𝓖₁) and M(𝓖₂), respectively, such that (M(𝓖₁),τ₁)** is isometrically...

Lp multipliers and their H1-L1 estimates on the Heisenberg group.

Chin-Cheng Lin (1995)

Revista Matemática Iberoamericana

We give a Hörmander-type sufficient condition on an operator-valued function M that implies the Lp-boundedness result for the operator TM defined by (TMf)^ = Mf^ on the (2n + 1)-dimensional Heisenberg group Hn. Here ^ denotes the Fourier transform on Hn defined in terms of the Fock representations. We also show the H1-L1 boundedness of TM, ||TMf||L1 ≤ C||f||H1, for Hn under the same hypotheses of Lp-boundedness.

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