We present sensitive 3.0 cm JVLA radio continuum observations of six regions of low-mass star formation that include twelve young brown dwarfs (BDs) and four young BD candidates. We detect a total of 49 compact radio sources in the fields observed, of which 24 have no reported counterparts and are considered new detections. Twelve of the radio sources show variability in timescales of weeks to months, suggesting gyrosynchrotron emission produced in active magnetospheres. Only one of the target BDs, FU Tau A, was detected. However, we detected radio emission associated with two of the BD candidates, WL 20S and CHLT 2. The radio flux densities of the sources associated with these BD candidates are more than an order of magnitude larger than expected for a BD and suggest a revision of their classification. In contrast, FU Tau A falls on the well-known correlation between radio luminosity and bolometric luminosity, suggesting that the emission comes from a thermal jet and that this BD seems to be forming as a scaled-down version of low-mass stars.