Bilinear $\theta$-type Calderón-Zygmund operators and its commutator on generalized weighted Morrey spaces over RD-spaces

Abstract

An RD-space $\mathcal{X}$ is a space of homogeneous type in the sense of Coifman and Weiss with the additional property that a reverse doubling property holds in $\mathcal{X}$. In this setting, the authors establish the boundedness of bilinear $\theta$-type Calderón-Zygmund operator $T_{\theta }$ and its commutator $[b_1,b_2,T_{\theta }]$ generated by the function $b_1,b_2\in BMO(\mu )$ and $T_{\theta }$ on generalized weighted Morrey space ${\mathcal{M}}^{p,\varphi }(\omega )$ and generalized weighted weak Morrey space $W{\mathcal{M}}^{p,\varphi }(\omega )$ over RD-spaces.

20 pages