  We use the image solution technique to compute the leading order
frequency-dependent self-mobility function of a small solid particle moving
perpendicular to the surface of a spherical capsule whose membrane possesses
shearing and bending rigidities. Comparing our results with those obtained
earlier for an infinitely extended planar elastic membrane, we find that
membrane curvature leads to the appearance of a prominent additional peak in
the mobility. This peak is attributed to the fact that the shear resistance of
the curved membrane involves a contribution from surface-normal displacements
which is not the case for planar membranes. In the vanishing frequency limit,
the particle self-mobility near a no-slip hard sphere is recovered only when
the membrane possesses a non-vanishing resistance towards shearing. We further
investigate capsule motion, finding that the pair-mobility function is solely
determined by membrane shearing properties. Our analytical predictions are
validated by fully resolved boundary integral simulations where a very good
agreement is obtained.
