(abbreviated) We aim to determine the masses of the envelopes, disks, and central stars of young stellar objects (YSOs) in the Class I stage. We observed the embedded Class I objects IRS 63 and Elias 29 in the rho Ophiuchi star-forming region with the Submillimeter Array (SMA) at 1.1 mm. IRS 63 and Elias 29 are both clearly detected in the continuum, with peak fluxes of 459 resp. 47 mJy/beam. The continuum emission toward Elias 29 is clearly resolved, whereas IRS 63 is consistent with a point source down to a scale of 3 arcsec (400 AU). The SMA data are combined with single-dish data, and disk masses of 0.055 and >= 0.007 MSun and envelope masses of 0.058 and >= 0.058 MSun are empirically determined for IRS 63 and Elias 29, respectively. The disk+envelope systems are modelled with the axisymmetric radiative-transfer code RADMC, yielding disk and envelope masses that differ from the empirical results by factors of a few. HCO+ J = 3-2 is detected toward both sources, HCN J = 3-2 is not. The HCO+ position-velocity diagrams are indicative of Keplerian rotation. For a fiducial inclination of 30 degrees, we find stellar masses of 0.37 +/- 0.13 and 2.5 +/- 0.6 MSun for IRS 63 and Elias 29, respectively. We conclude that the sensitivity and spatial resolution of the SMA at 1.1 mm allow a good separation of the disks around Class I YSOs from their circumstellar envelopes and environments, and the spectral resolution makes it possible to resolve their dynamical structure and estimate the masses of the central stars. The ratios of the envelope and disk masses are found to be 0.2 and 6 for IRS 63 and Elias 29, respectively. This is lower than the values for Class 0 sources, which have Menv/Mdisk >= 10, suggesting that this ratio is a tracer of the evolutionary stage of a YSO.
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