We have conducted a deep radio survey with the Very Large Array at 1.4 GHz of a region containing the Hubble Deep Field. This survey overlaps previous observations at 8.5 GHz allowing us to investigate the radio spectral properties of microjansky sources to flux densities greater than 40 μJy at 1.4 GHz and greater than 8 μJy at 8.5 GHz. A total of 371 sources have been catalogued at 1.4 GHz as part of a complete sample within 20 of the HDF. The differential source count for this region is only

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... arginally sub-Euclidean and is given by n(S) = (8.3 ± 0.4) S^-2.4 ± 0.1 sr^-1Jy^-1. Above about 100 μJy the radio source count is systematically lower in the HDF as compared to other fields. We conclude that there is clustering in our radio sample on size scales of 1 - 40Ṫhe 1.4 GHz selected sample shows that the radio spectral indices are preferentially steep (α̅_1.4 = 0.85 ) and the sources are moderately extended with average angular size θ = 1.8 . Optical identification with disk-type systems at z ∼ 0.5-0.8 suggests that synchrotron emission, produced by supernovae remnants, is powering the radio emission in the majority of sources. The 8.5 GHz sample contains primarily moderately flat spectrum sources (α̅_8.5 = 0.35), with less than 15 optically thin bremsstrahlung over synchrotron radiation in these distant star-forming galaxies.