  Starting from a Whitney decomposition of a symmetric cone $\Omega$, analog to
the dyadic partition $[2^j, 2^{j+1})$ of the positive real line, in this paper
we develop an adapted Littlewood-Paley theory for functions with spectrum in
$\Omega$. In particular, we define a natural class of Besov spaces of such
functions, $B^{p,q}_\nu$, where the role of usual derivation is now played by
the generalized wave operator of the cone $\Delta(\frac{\partial}{\partial
x})$. Our main result shows that $B^{p,q}_\nu$ consists precisely of the
distributional boundary values of holomorphic functions in the Bergman space
$A^{p,q}_\nu(T_\Omega)$, at least in a ``good range'' of indices $1\leq
q<q_{\nu,p}$. We obtain the sharp $q_{\nu,p}$ when $p\leq 2$, and conjecture a
critical index for $p>2$. Moreover, we show the equivalence of this problem
with the boundedness of Bergman projectors $P_\nu\colon L^{p,q}_\nu\to
A^{p,q}_\nu$, for which our result implies a positive answer when
$q_{\nu,p}'<q<q_{\nu,p}$. This extends to general cones previous work of the
authors in the light-cone. Finally, we conclude the paper with a finer analysis
in light-cones, for which we establish a link between our conjecture and the
cone multiplier problem. Moreover, using recent work by Tao, Vargas and Wolff,
we improve in dimension 3 the range of $q$'s for which the Bergman projection
is bounded.
