AbstractThe inclusions between the Besov spaces $$B^q$$
B
q
, the Bloch space $$\mathcal {B}$$
B
and the standard weighted Bergman spaces $$A^p_{\alpha}$$
A
α
p
are completely understood, but the norms of the corresponding inclusion operators are in general unknown. In this work, we compute or estimate asymptotically the norms of these inclusions.
AbstractIn the present paper, we first study the wandering subspace property of the shift operator on the $$I_{a}$$
I
a
type zero based invariant subspaces of the weighted Bergman spaces $$L_{a}^{2}(dA_{n})(n=0,2)$$
L
a
2
(
d
A
n
)
(
n
=
0
,
2
)
via the spectrum of some Toeplitz operators on the Hardy space $$H^{2}$$
H
2
. Second, we give examples to show that Shimorin’s condition for the shift operator fails on the $$I_{a}$$
I
a
type zero based invariant subspaces of the weighted Bergman spaces $$L_{a}^{2}(dA_{\alpha })(\alpha >0)$$
L
a
2
(
d
A
α
)
(
α
>
0
)
.
AbstractWe determine the eigenvalues of certain “fundamental” K-invariant Toeplitz type operators on weighted Bergman spaces over bounded symmetric domains $$D=G/K,$$
D
=
G
/
K
,
for the irreducible K-types indexed by all partitions of length $$r={\mathrm {rank}}(D)$$
r
=
rank
(
D
)
.
Toeplitz Operators on Weighted Bergman Spaces Induced by a Class of Radial Weights
