  We present a CARMA 1.3 mm continuum survey toward 9 Class 0 protostars in the
Perseus molecular cloud at $\sim$0.3$^{\prime\prime}$ (70 AU) resolution. This
study approximately doubles the number of Class 0 protostars observed with
spatial resolutions $<$ 100 AU at millimeter wavelengths, enabling the presence
of protostellar disks and proto-binary systems to be probed. We detect
flattened structures with radii $>$ 100 AU around 2 sources (L1448 IRS2 and
Per-emb-14) and these sources may be strong disk candidates.
Marginally-resolved structures with position angles within 30$^{\circ}$ of
perpendicular to the outflow are found toward 3 protostars (L1448 IRS3C, IRAS
03282+3035, and L1448C) and are considered disk candidates. Two others (L1448
IRS3B and IRAS 03292+3039) have resolved structure, possibly indicative of
massive inner envelopes or disks; L1448 IRS3B also has a companion separated by
0.9$^{\prime\prime}$ ($\sim$210 AU). IC348-MMS does not have well-resolved
structure and the candidate first hydrostatic core L1451-MMS is marginally
resolved on 1$^{\prime\prime}$ scales. The strong disk candidate sources were
followed-up with C$^{18}$O ($J=2\rightarrow1$) observations, detecting velocity
gradients consistent with rotation, but it is unclear if the rotation is
Keplerian. We compare the observed visibility amplitudes to radiative transfer
models, finding that visibility amplitude ratios suggest a compact component
(possibly a disk) is necessary for 5 of 9 Class 0 sources; envelopes alone may
explain the other 4 systems. We conclude that there is evidence for the
formation of large disks in the Class 0 phase with a range of radii and masses
dependent upon their initial formation conditions.
