Extrapolation in Variable Lebesgue Spaces

Abstract

In this chapter we develop a general theory for proving norm inequalities for the other classical operators in harmonic analysis. Our main result is a powerful generalization of the Rubio de Francia extrapolation theorem. This approach, first developed in [22] and then treated as part of a more general framework in [27], lets us use the theory of weighted norm inequalities to prove the corresponding estimates in variable Lebesgue spaces. This greatly reduces the work required, since it lets us use the well-developed theory of weights.