Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2403.11467 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
Tabla de Contenidos:
- Let $\mathbb{H}^{n}$ be the Heisenberg group. For $0 \leq α< Q=2n+2$ and $N \in \mathbb{N}$ we consider exponent functions $p(\cdot) : \mathbb{H}^{n} \to (0, +\infty)$, which satisfies Hölder conditions, such that $\frac{Q}{Q+N} < p_{-} \leq p(\cdot) \leq p_{+} < \frac{Q}α$. In this article we prove the $H^{p(\cdot)}(\mathbb{H}^{n}) \to L^{q(\cdot)}(\mathbb{H}^{n})$ and $H^{p(\cdot)}(\mathbb{H}^{n}) \to H^{q(\cdot)}(\mathbb{H}^{n})$ boundedness of convolution operators with kernels of type $(α, N)$ on $\mathbb{H}^{n}$, where $\frac{1}{q(\cdot)} = \frac{1}{p(\cdot)} - \fracα{Q}$. In particular, the Riesz potential on $\mathbb{H}^{n}$ satisfies such estimates.