论文标题
某些操作员在RD空间上的大广义加权莫雷空间的界限
Boundedness of some operators on grand generalized weighted Morrey spaces on RD-spaces
论文作者
论文摘要
本文的目的是在宏伟的加权Morrey空间上获得某些操作员的界限$ \ MATHCAL {L}^{p），ϕ}}_φ（ω）$在RD空间上。在假设功能$φ$和$ ϕ $满足某些条件下的假设下，作者证明，Hardy-Little Wood Maximal Operator和$θ$-TypeCalderón-Zygmund操作员在宏伟的广义加权Morrey Spaces $ \ Mathcal {L}^{l}^{p），ϕ} _或$。此外，由$θ$ -Typecalderón-Zygmund运算符$t_θ$和$ b \ in \ mathrm {bmo}（μ）$在空间$ \ nathcal {l}^p）上生成$θ$-typeCalderón-zygmund运算符$t_θ$和$ b \ in comptecalderón-zygmund操作员$t_θ$和$ b \ in Complator $ [B，t_θ] $的界限。关于宏伟的加权莫雷空间的结果，即使对于欧几里得空间领域，也是新的。
The aim of this paper is to obtain the boundedness of some operator on grand generalized weighted Morrey spaces $\mathcal{L}^{p),ϕ}_φ(ω)$ over RD-spaces. Under assumption that functions $φ$ and $ϕ$ satisfy certain conditions, the authors prove that Hardy-Littlewood maximal operator and $θ$-type Calderón-Zygmund operator are bounded on grand generalized weighted Morrey spaces $\mathcal{L}^{p),ϕ}_φ(ω)$. Moreover, the boundedness of commutator $[b,T_θ]$ which is generated by $θ$-type Calderón-Zygmund operator $T_θ$ and $b\in\mathrm{BMO}(μ)$ on spaces $\mathcal{L}^{p),ϕ}_φ(ω)$ is also established. The results regarding the grand generalized weighted Morrey spaces is new even for domains of Euclidean spaces.
