AbstractCompact differences of two weighted composition operators acting from the weighted Bergman space $$A^p_{\omega }$$
A
ω
p
to another weighted Bergman space $$A^q_{\nu }$$
A
ν
q
, where $$0<p\le q<\infty $$
0
<
p
≤
q
<
∞
and $$\omega ,\nu $$
ω
,
ν
belong to the class $${\mathcal {D}}$$
D
of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proof a new description of q-Carleson measures for $$A^p_{\omega }$$
A
ω
p
, with $$\omega \in {\mathcal {D}}$$
ω
∈
D
, in terms of pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_{\alpha }$$
A
α
p
with $$-1<\alpha <\infty $$
-
1
<
α
<
∞
to the setting of doubling weights.