We report on a search for persistent radio emission from the one-off fast radio burst (FRB) 20190714A, as well as from two repeating FRBs, 20190711A and 20171019A, using the MeerKAT radio telescope. For FRB 20171019A, we also conducted simultaneous observations with the High-Energy Stereoscopic System (H.E.S.S.) in very high-energy gamma rays and searched for signals in the ultraviolet, optical, and X-ray bands. For this FRB, we obtain a UV flux upper limit of 1.39 × 10-16 erg, cm-2, s-1Å-1, X-ray limit of ~6.6 × 10-14~erg, cm-2, s-1 and a limit on the very high energy gamma-ray flux Φ (E> 120, GeV) < 1.7× 10-12, erg, cm-2, s-1. We obtain a radio upper limit of ∼15 μJy beam-1 for persistent emission at the locations of both FRBs 20190711A a...