On the relation of Carleson's embedding and the maximal theorem in the context of Banach space geometry

  • Tuomas Hytönen
  • Mikko Kemppainen

Abstract

Hytönen, McIntosh and Portal (J. Funct. Anal., 2008) proved two vector-valued generalizations of the classical Carleson embedding theorem, both of them requiring the boundedness of a new vector-valued maximal operator, and the other one also the type $p$ property of the underlying Banach space as an assumption. We show that these conditions are also necessary for the respective embedding theorems, thereby obtaining new equivalences between analytic and geometric properties of Banach spaces.
Published
2011-12-01
How to Cite
Hytönen, T., & Kemppainen, M. (2011). On the relation of Carleson’s embedding and the maximal theorem in the context of Banach space geometry. MATHEMATICA SCANDINAVICA, 109(2), 269-284. https://doi.org/10.7146/math.scand.a-15189
Section
Articles