A generalized Kolmogorov inequality for the Hilbert transform

If $f\in L^1(\mathbf{R}^1;(1+\vert x\vert)^{-1}dx)$ we can define the Hilbert transform $Hf$ almost everywhere (Lebesgue) and obtain an estimate for $\mu\{x:\,\vert Hf(x)\vert\ge \alpha\}$ where $\mu$ is a suitable finite measure. The classical Kolmogorov inequality for the Lebesgue measure of $\{x:\,\vert Hf(x)\vert\ge\alpha\}$ is obtained by a scaling argument.