Boundedness of vector-valued B-singular integral operators in Lebesgue spaces

We study the vector-valued B-singular integral operators associated with the Laplace-Bessel differential operator $$\triangle_{B}=\sum\limits_{k=1}^{n-1}\frac{\partial^{2}}{\partial x_{k}^{2}}+(\frac{\partial^{2}}{\partial x_{n}^{2}}+\frac{2v}{x_{n}}\frac{\partial}{\partial x_{n}}) , v>0.$$ We prove the boundedness of vector-valued B-singular integral operators A from $L_{p,v}(\mathbb{R}_{+}^{n}, H_{1}) \,{\rm to}\, L_{p,v}(\mathbb{R}_{+}^{n}, H_{2}),$ 1 < p < ∞, where H1 and H2 are separable Hilbert spaces.