TY  - JOUR
ID  - Rocha2026
LB  - Rocha2026
AU  - Rocha, Pablo
TI  - Calderón-Hardy type spaces and the Heisenberg sub-Laplacian
ST  - Calderón-Hardy type spaces and the Heisenberg sub-Laplacian
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2026
VL  - 46
IS  - 1
SP  - 73
EP  - 99
DO  - https://doi.org/10.7494/OpMath.202512221
UR  - https://doi.org/10.7494/OpMath.202512221
AB  - For \(0 \lt p \leq 1 \lt q \lt \infty\) and \(\gamma \gt 0\), we introduce the Calderón-Hardy spaces \(\mathcal{H}^{p}_{q,\gamma}(\mathbb{H}^{n})\) on the Heisenberg group \(\mathbb{H}^{n}\), and show for every \(f \in H^{p}(\mathbb{H}^{n})\) that the equation \[\mathcal{L}F=f\] has a unique solution \(F\) in \(\mathcal{H}^{p}_{q,2}(\mathbb{H}^{n})\), where \(\mathcal{L}\) is the sub-Laplacian on \(\mathbb{H}^{n}\), \[1 \lt q \lt \frac{n+1}{n} \quad \text{and} \quad (2n+2)\left(2+\frac{2n+2}{q}\right)^{-1} \lt p \leq 1.\]
KW  - Calderón-Hardy type spaces
KW  - Hardy type spaces
KW  - atomic decomposition
KW  - Heisenberg group
KW  - sub-Laplacian
SN  - 1232-9274
ER  -