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We study the vector-valued B-singular integral operators associated with the Laplace-Bessel differential operator △B=∑k=1n−1∂ 2∂x k 2+(∂2∂x n 2+2vxn∂∂x n),v>0. $${▵}_B=\sum _{k=1}^{n-1}\frac{{\partial }^2}{\partial x_k^2}+(\frac{{\partial }^2}{\partial x_n^2}+\frac{2v}{x_n}\frac{\partial }{\partial x_n}),v>0.$$ We prove the boundedness of vector-valued B-singular integral operators A from [...] Lp,v(R+n,H1)toLp,v(R+n,H2), $L_{p,v}({ℝ}_{+}^n,H_1)\mathrm{to}{L}_{p,v}({ℝ}_{+}^n,H_2),$ 1 < p < ∞, where H1 and H2 are separable Hilbert spaces.

We obtain the global weighted Morrey-type regularity of the solution of the regular oblique derivative problem for linear uniformly parabolic operators with VMO coefficients. We show that if the right-hand side of the parabolic equation belongs to certain generalized weighted Morrey space Mp,ϕ(Q, w), than the strong solution belongs to the generalized weighted Sobolev- Morrey space [...] W˙2,1p,φ(Q,ω)${\dot{W}}_{2,1}^{p,\varphi }\left(Q,\omega \right)$.