Calderón-Hardy type spaces and the Heisenberg sub-Laplacian

2025/05/17 by Rocha, Pablo · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.12163

Abstract

For 0 < p ≤ 1 < q < ∞ and γ> 0, we introduce the Calderón-Hardy spaces H^p_{q, γ}(ℍⁿ) on the Heisenberg group ℍⁿ, and show for every f ∈ H^p(ℍⁿ) that the equation L F = f has a unique solution F in H^p_{q, 2}(ℍⁿ), where L is the sublaplacian on ℍⁿ, 1 < q < (n+1)/(n) and (2n+2) (2 + (2n+2)/(q))^-1 < p ≤ 1.

Citations

• Fundamental solutions for powers of the Heisenberg sub-Laplacian
• Hp spaces of several variables

Cited by

• Variable Calderón-Hardy spaces on the Heisenberg group

Related

• Variable Calderón-Hardy spaces on the Heisenberg group
• Generalizations of a Laplacian-Type Equation in the Heisenberg Group and a Class of Grushin-Type Spaces
• Dirichlet problem for Schrödinger operators on Heisenberg groups
• Hardy spaces and quasiconformal maps in the Heisenberg group
• Geometric Hardy and Hardy-Sobolev inequalities on Heisenberg groups