Localization principle for Triebel-Lizorkin spaces on spaces of homogeneous type.
The author establishes the localization principle for the Triebel-Lizorkin spaces on spaces of homogeneous type.
The author establishes the localization principle for the Triebel-Lizorkin spaces on spaces of homogeneous type.
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...
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.
Let £ denote the sub-Laplacian on the Heisenberg group Hm. We prove that ei√£ / (1 - £)α/2 extends to a bounded operator on Lp(Hm), for 1 ≤ p ≤ ∞, when α > (d - 1) |1/p - 1/2|.