We study theoretically the velocity cross-correlations of a viscous fluid confined in a slit between two viscoelastic media. We analyze the effect of these correlations on the motions of particles suspended in the fluid. The compliance of the confining boundaries gives rise to a long-ranged pair correlation, decaying only as $1/r$ with the interparticle distance $r$. We show how this long-ranged effect may be used to extract the viscoelastic properties of the confining media without embedding tracer particles in them. We discuss the remarkable robustness of such a potential technique with respect to details of the confinement, and its expected statistical advantages over standard two-point microrheology.
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