Bilinear Θ$\Theta$‐type Calderón–Zygmund operators and their commutators on product generalized fractional mixed Morrey spaces

The aim of this paper is to investigate the boundedness of the bilinear θ$\theta$‐type Calderón–Zygmund operator and its commutator on the product of generalized fractional mixed Morrey spaces. Under assumption that the positive and increasing functions φ(·)$\varphi (\cdot)$ defined on [0,∞)$[0,\infty)$ satisfy doubling conditions, we prove that the bilinear θ$\theta$‐type Calderón–Zygmund operator T∼θ$\widetilde{T}_{\theta }$ is bounded from the product of generalized fractional mixed Morrey spaces Lp⃗1,η1,φ(Rn)×Lp⃗2,η2,φ(Rn)$L^{\vec{p}_{1},\eta _{1},\varphi }({\bf R}^{n})\times L^{\vec{p}_{2},\eta _{2},\varphi }({\bf R}^{n})$ into spaces Lp⃗,η,φ(Rn)$L^{\vec{p},\eta,\varphi }({\bf R}^{n})$, where p⃗1=(p11,…,p1n)$\vec{p}_{1}=(p_{11},\ldots ,p_{1n})$, p⃗2=(p21,…,p2n)$\vec{p}_{2}=(p_{21},\ldots ,p_{2n})$, p⃗=(p1,…,pn)$\vec{p}=(p_{1},\ldots ,p_{n})$, 1p⃗1+1p⃗2=1p⃗$\frac{1}{\vec{p}_{1}}+\frac{1}{\vec{p}_{2}}=\frac{1}{\vec{p}}$ for 1