Variable Calderón-Hardy spaces on the Heisenberg group

2025/05/21 by Pablo Rocha, Rocha, Pablo
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.2505.15760

openalex publication_date 2025/05/21 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

Let ℍⁿ be the Heisenberg group and Q = 2n+2. For 1 < q < ∞, γ> 0 and an exponent function p(⋅) on ℍⁿ, which satisfy log-Hölder conditions, with 0 < p_- ≤ p₊ < ∞, we introduce the variable Calderón-Hardy spaces H^p(⋅)_{q, γ}(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 Q (2 + (Q)/(q))^-1 < \underlinep.

Citations

• Calderón-Hardy type spaces and the Heisenberg sub-Laplacian
• Convolution operators and variable Hardy spaces on the Heisenberg group

Related

• Calderón-Hardy type spaces and the Heisenberg sub-Laplacian
• Convolution operators and variable Hardy spaces on the Heisenberg group
• Calderón-Hardy Spaces with variable exponents and the Solution of the Equation Δ^m F = f for f ∈ H^p(⋅)(ℝⁿ)
• Dirichlet problem for Schrödinger operators on Heisenberg groups
• Hardy spaces and quasiconformal maps in the Heisenberg group