In this paper, we provide a complete function theoretic characterizations for boundedness and compactness of difference of weighted composition operators from the space of Cauchy integral transforms to logarithmic weighted-type spaces. Surprisingly, an interesting feature of these characterizations is that they are free from pseudo-hyperbolic distance between $\varphi(z)$ and $\psi(z)$, which is different from the previous characterizations of difference of weighted composition operators acting between different holomorphic function spaces.
"Difference of Weighted Composition Operators on the Space of Cauchy Integral Transforms." Taiwanese J. Math. 22 (6) 1435 - 1450, December, 2018. https://doi.org/10.11650/tjm/180404