A note on Rubio de Francia's extrapolation in tent spaces and applications

Abstract: The Rubio de Francia extrapolation theorem is a very powerful result which states that in order to show that certain operators satisfy weighted norm inequalities with Muckenhoupt weights it suffices to see that the corresponding inequalities hold for some fixed exponent, for instance $p=2$. In this paper we extend this result and show that this extrapolation principle allows one to obtain weighted estimates in tent spaces. From our extrapolation result we automatically derive new estimates (and reprove some other) concerning Calder\'on-Zygmund operators, operators associated with the Kato conjecture, or fractional operators.