  We give Feffermain-Stein type inequalities related to mixed estimates for
Calder\'on-Zygmund operators. More precisely, given $\delta>0$, $q>1$,
$\varphi(z)=z(1+\log^+z)^\delta$, a nonnegative and locally integrable function
$u$ and $v\in \mathrm{RH}_\infty\cap A_q$, we prove that the inequality
  \[uv\left(\left\{x\in \mathbb{R}^n:
\frac{|T(fv)(x)|}{v(x)}>t\right\}\right)\leq
\frac{C}{t}\int_{\mathbb{R}^n}|f|\left(M_{\varphi,
v^{1-q'}}u\right)M(\Psi(v))\]
  holds with
$\Psi(z)=z^{p'+1-q'}\mathcal{X}_{[0,1]}(z)+z^{p'}\mathcal{X}_{[1,\infty)}(z)$,
for every $t>0$ and every $p>\max\{q,1+1/\delta\}$. This inequality provides a
more general version of mixed estimates for Calder\'on-Zygmund operators proved
in \cite{CruzUribe-Martell-Perez}. It also generalizes the Fefferman-Stein
estimates given in \cite{P94} for the same operators.
  We further get similar estimates for operators of convolution type with
kernels satisfying an $L^\Phi-$H\"ormander condition, generalizing some
previously known results which involve mixed estimates and Fefferman-Stein
inequalities for these operators.
