On a general Lie group G endowed with a sub-Riemannian structure and of local dimension d, we characterize the pointwise multipliers of Triebel–Lizorkin spaces Fp,q α for p, q ∈ (1, ∞) and α > d/p, and those of Besov spaces Bp,q α for q ∈ [1, ∞], p >d and d/p <α < 1. When G is stratified, we extend the latter characterization to all p, q ∈ [1, ∞] and α > d/p.
Pointwise multipliers for Triebel–Lizorkin and Besov spaces on Lie groups
Bruno T.;
2023-01-01
Abstract
On a general Lie group G endowed with a sub-Riemannian structure and of local dimension d, we characterize the pointwise multipliers of Triebel–Lizorkin spaces Fp,q α for p, q ∈ (1, ∞) and α > d/p, and those of Besov spaces Bp,q α for q ∈ [1, ∞], p >d and d/p <α < 1. When G is stratified, we extend the latter characterization to all p, q ∈ [1, ∞] and α > d/p.
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