Bilinear θ-type Calderón–Zygmund operators and its commutator on generalized weighted Morrey spaces over RD-spaces

Abstract

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