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.
Toeplitz operators and Carleson measures on parabolic Bergman spaces