Abstract
It is well-known that in Banach spaces with finite cotype, the -bounded and -bounded families of operators coincide. If in addition is a Banach lattice, then these notions can be expressed as square function estimates. It is also clear that -boundedness implies -boundedness. In this note we show that all other possible inclusions fail. Furthermore, we will prove that -boundedness is stable under taking adjoints if and only if the underlying space is -convex.
Funding Statement
The first named author is supported by NCN grant Dec-2012/05/B/ST1/00412. The second author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation for Scientific Research (NWO). The third named author is supported by a grant from the Graduierten Kolleg 1294DFG.
Citation
Stanislaw Kwapień. Mark Veraar. Lutz Weis. "-Boundedness versus -boundedness." Ark. Mat. 54 (1) 125 - 145, April 2016. https://doi.org/10.1007/s11512-015-0223-1
Information