  The issue of non-analytic corrections to the Fermi-liquid behavior is
revisited. Previous studies have indicated that the corrections to the
Fermi-liquid forms of the specific heat and the static spin susceptibility
scale as $T^{D}$ and $T^{D-1}$, respectively (with extra logarithms for
$D=1,3$). In addition, the non-uniform spin susceptibility is expected to
depend on the bosonic momentum $Q$ in a non-analytic way, i.e., as $Q^{D-1}$
(again with extra logarithms for $D=1,3$). It is shown that these non-analytic
corrections originate from the universal singularities in the dynamical bosonic
response functions of a generic Fermi liquid. In contrast to the leading,
Fermi-liquid forms which depend on the interaction averaged over the Fermi
surface, the non-analytic corrections are parameterized by only two coupling
constants, which are the components of the interaction potential at momentum
transfers $q=0$ and $q=2k_F$. For 3D systems, a recent result of Belitz,
Kirkpatrick and Vojta for the spin susceptibility is reproduced and the issue
why a non-analytic momentum dependence of the non-uniform spin susceptibility
($Q^{2}\ln |Q|$) is \emph{not}paralleled by a non-analyticity in the $T-$
dependence ($T^2$) is clarified. For the case of a 2D system with a
finite-range interaction, explicit forms of the corrections to the specific
heat ($\propto T^2$), uniform ($\propto T$) and non-uniform ($\propto |Q|$)
spin susceptibilities are obtained. It is shown that previous calculations of
the temperature dependences of these quantities in 2D were incomplete. Some of
the results and conclusions of this paper have recently been announced in a
short communication [A. V. Chubukov and D. L. Maslov, cond-mat/0304381].
