AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$
A
ω
p
to the Lebesgue space $$L^q_\nu $$
L
ν
q
, where $$0<q<p<\infty $$
0
<
q
<
p
<
∞
and $$\omega $$
ω
belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$
A
ω
p
, with $$p>q$$
p
>
q
and "Equation missing", involving 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. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.
Carleson Measures and Toeplitz Operators