  Hot dust-obscured galaxies (hot DOGs) are a rare class of hyperluminous
infrared galaxies identified with the Wide-field Infrared Survey Explorer
(WISE) satellite. The majority of them is at high redshifts (z~2-3), at the
peak epoch of star formation in the Universe. Infrared, optical, radio, and
X-ray data suggest that hot DOGs contain heavily obscured, extremely luminous
active galactic nuclei (AGN). This class may represent a short phase in the
life of the galaxies, signifying the transition from starburst- to
AGN-dominated phases. Hot DOGs are typically radio-quiet, but some of them show
mJy-level emission in the radio (microwave) band. We observed four hot DOGs
using the technique of very long baseline interferometry (VLBI). The 1.7-GHz
observations with the European VLBI Network (EVN) revealed weak radio features
in all sources. The radio is free from dust obscuration and, at such high
redshifts, VLBI is sensitive only to compact structures that are characteristic
of AGN activity. In two cases (WISE J0757+5113, WISE J1603+2745), the flux
density of the VLBI-detected components is much smaller than the total flux
density, suggesting that ~70-90 per cent of the radio emission, while still
dominated by AGN, originates from angular scales larger than probed by the EVN.
The source WISE J1146+4129 appears a candidate compact symmetric object, and
WISE J1814+3412 shows a 5.1-kpc double structure, reminiscent of hot spots in a
medium-sized symmetric object. Our observations support that AGN residing in
hot DOGs may be genuine young radio sources where starburst and AGN activities
coexist.
