非齐性广义Morrey空间上双线性强奇异Calder\'{o}n-Zygmund算子及交换子

Bilinear Strongly Singular Calder\'{o}n-Zygmund Operators and Their Commutators on Non-Homogeneous Generalized Morrey Spaces

中文关键词:  非齐性度量测度空间  双线性强奇异Calder\'{o}n-Zygmund算子  交换子  $\widetilde{\mathrm{RBMO}}(\mu)$空间  广义Morrey 空间

英文关键词:non-homogeneous metric measure space  bilinear strongly singular Calder\'{o}n-Zygmund operator  commutator  space $\widetilde{\mathrm{RBMO}}(\mu)$  generalized Morrey space

中文摘要:

      本文的主要建立非齐性度量测度空间上双线性强奇异积分算子$\widetilde{T}$及交换子$\widetilde{T}_{b_{1},b_{2}}$在广义Morrey空间$M^{u}_{p}(\mu)$上的有界性. 在假设Lebesgue可测函数$u, u_{1}, u_{2}\in\mathbb{W}_{\tau}$, $u_{1}u_{2}=u$,且$\tau\in(0,2)$. 证明了算子$\widetilde{T}$是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到空间$M^{u}_{p}(\mu)$有界的, 也是从乘积空间$M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$到广义弱Morrey空间$WM^{u}_{p}(\mu)$有界的,其中$\frac{1}{p}=\frac{1}{p_{1}}+\frac{1}{p_{2}}$及$1

英文摘要:

      The main goal of this paper is to establish the boundedness of bilinear strongly singular operator $\widetilde{T}$ and its commutator $\widetilde{T}_{b_{1},b_{2}}$ on generalized Morrey spaces $M^{u}_{p}(\mu)$ over non-homogeneous metric measure spaces. Under assumption that the Lebesgue measurable functions $u, u_{1}$ and $u_{2}$ belong to $\mathbb{W}_{\tau}$ for $\tau\in(0,2)$, and $u_{1}u_{2}=u$. The authors prove that $\widetilde{T}$ is bounded from product spaces $M^{u_{1}}_{p_{1}}(\mu)\times M^{u_{2}}_{p_{2}}(\mu)$ into spaces $M^{u}_{p}(\mu)$, where $\frac{1}{p}=\frac{1}{p_{1}}+\frac{1}{p_{2}}$ with $1