We present Karl G. Jansky Very Large Array (VLA) observations of the 7 mm continuum emission from the disk surrounding the young star LkCa 15. The observations achieve an angular resolution of 70 mas and spatially resolve the circumstellar emission on a spatial scale of 9 AU. The continuum emission traces a dusty annulus of 45 AU in radius that is consistent with the dust morphology observed at shorter wavelengths. The VLA observations also reveal a compact source at the center of the disk, possibly due to thermal emission from hot dust or ionized gas located within a few AU from the central star. No emission is observed between the star and the dusty ring, and, in particular, at the position of the candidate protoplanet LkCa 15 b. By comparing the observations with theoretical models for circumplanetary disk emission, we find that if LkCa~15~b is a massive planet (>5 M_J) accreting at a rate greater than 1.e-6 M_J yr^{-1}, then its circumplanetary disk is less massive than 0.1 M_J, or smaller than 0.4 Hill radii. Similar constraints are derived for any possible circumplanetary disk orbiting within 45 AU from the central star. The mass estimate are uncertain by at least one order of magnitude due to the uncertainties on the mass opacity. Future ALMA observations of this system might be able to detect circumplanetary disks down to a mass of 5.e-4 M_J and as small as 0.2 AU, providing crucial constraints on the presence of giant planets in the act of forming around this young star.
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