RT Journal Article
T1 Composition operators on hardy spaces on Lavrentiev domains
A1 Gallardo Gutiérrez, Eva Antonia
A1 González, María J.
A1 Nicolau, Arthur
AB For any simply connected domain., we prove that a Littlewood type inequality is necessary for boundedness of composition operators on H-p(Omega), 1 <= p < infinity, whenever the symbols are finitely-valent. Moreover, the corresponding "little-oh" condition is also necessary for the compactness. Nevertheless, it is shown that such an inequality is not sufficient for characterizing bounded composition operators even induced by univalent symbols. Furthermore, such inequality is no longer necessary if we drop the extra assumption on the symbol of being finitely-valent. In particular, this solves a question posed by Shapiro and Smith (2003). Finally, we show a striking link between the geometry of the underlying domain. and the symbol inducing the composition operator in H-p(Omega), and in this sense, we relate both facts characterizing bounded and compact composition operators whenever. is a Lavrentiev domain.
PB American Mathematical Society
SN 0002-9947
YR 2008
FD 2008
LK https://hdl.handle.net/20.500.14352/50599
UL https://hdl.handle.net/20.500.14352/50599
LA eng
NO Plan Nacional I+D
NO Gobierno de Aragón
DS Docta Complutense
RD 17 abr 2025