Mixed weak estimates of Sawyer type for generalized maximal operators
Mixed weak estimates of Sawyer type for generalized maximal operators
We study mixed weak estimates of Sawyer type for maximal operators associated to the family of Young functions $\Phi(t)=t^r(1+\log^+t)^{\delta}$, where $r\geq 1$ and $\delta\geq 0$. More precisely, if $u$ and $v^r$ are $A_1$ weights, and $w$ is defined as $w=1/\Phi(v^{-1})$ then the following estimate \[uw\left(\left\{x\in \mathbb{R}^n: \frac{M_\Phi(fv)(x)}{v(x)} > t\right\}\right) \leq …