Publication at Faculty of Mathematics and Physics |
2023
Abstract
Rubio de Francia's extrapolation theorem constitutes a powerful result in the theory of weighted norm inequalities.
In particular, it allows one to deduce an inequality (often but not necessarily: the boundedness of an operator) on all weighted $L^p$ spaces with a range of $p$, by checking it just for one exponent $p$ (but all relevant weights).
This paper provides an analogous method for extrapolation of compactness.
In a relatively soft way, it recovers several recent results about compactness of operators on weighted spaces and also gives some new ones.