Variable Anisotropic Hardy Spaces with Variable Exponents
Let p(·) : ℝn → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝn introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp(·)(Θ) via the radial grand maximal function...
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/2d6d0498e3624958b869f2cd2228893a |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | Let p(·) : ℝn → (0, ∞] be a variable exponent function satisfying the globally log-Hölder continuous and let Θ be a continuous multi-level ellipsoid cover of ℝn introduced by Dekel et al. [12]. In this article, we introduce highly geometric Hardy spaces Hp(·)(Θ) via the radial grand maximal function and then obtain its atomic decomposition, which generalizes that of Hardy spaces Hp(Θ) on ℝn with pointwise variable anisotropy of Dekel et al. [16] and variable anisotropic Hardy spaces of Liu et al. [24]. As an application, we establish the boundedness of variable anisotropic singular integral operators from Hp(·)(Θ) to Lp(·)(ℝn) in general and from Hp(·)(Θ) to itself under the moment condition, which generalizes the previous work of Bownik et al. [6] on Hp(Θ). |
|---|