Abstract
AbstractWe establish that the Volterra-type integral operator $$J_b$$
J
b
on the Hardy spaces $$H^p$$
H
p
of the unit ball $${\mathbb {B}}^n$$
B
n
exhibits a rather strong rigid behavior. More precisely, we show that the compactness, strict singularity and $$\ell ^p$$
ℓ
p
-singularity of $$J_b$$
J
b
are equivalent on $$H^p$$
H
p
for any $$1 \le p < \infty $$
1
≤
p
<
∞
. Moreover, we show that the operator $$J_b$$
J
b
acting on $$H^p$$
H
p
cannot fix an isomorphic copy of $$\ell ^2$$
ℓ
2
when $$p \ne 2.$$
p
≠
2
.
Funder
National Natural Science Foundation of China
Academy of Finland
Engineering and Physical Sciences Research Council
Ministerio de Educación y Ciencia
Generalitat de Catalunya
Spanish Ministry of Economy and Competitiveness
Publisher
Springer Science and Business Media LLC
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