Recent ROSAT studies have identified a significant population of active gal
actic nuclei (AGNs) that are notably faint in soft X-rays relative to their
optical fluxes. Are these AGNs intrinsically X-ray weak or are they highly
absorbed? Brandt, Laor, & Wills have systematically examined the optical a
nd UV spectral properties of a well-defined sample of these soft X-ray-weak
(SXW) AGNs drawn from the Boroson & Green sample of all the Palomar Green
AGNs with z <0.5. We present ASCA observations of three of these SXW AGNs:
PG 1011-040, PG 1535+547 (Mrk 486), and PG 2112+059. In general, our ASCA o
bservations support the intrinsic absorption scenario for explaining soft X
-ray weakness; both PG 1535+547 and PG 2112+059 show significant column den
sities (N-H <approximate to> 10(22)-10(23) cm(-2)) of absorbing gas. Intere
stingly, PG 1011-040 shows no spectral evidence for X-ray absorption. The w
eak X-ray emission may result from very strong absorption of a partially co
vered source, or this AGN may be intrinsically X-ray weak. PG 2112+059 is a
broad absorption line (BAL) QSO, and we find it to have the highest X-ray
flux known of this class. It shows a typical power-law X-ray continuum abov
e 3 keV; this is the first direct evidence that BAL QSOs indeed have normal
X-ray continua underlying their intrinsic absorption. Finally, marked vari
ability between the ROSAT and ASCA observations of PG 1535+547 and PG 2112059 suggests that the soft X-ray-weak designation may be transient, and mul
tiepoch 0.1-10.0 keV X-ray observations are required to constrain variabili
ty of the absorber and continuum.