Matrix-weighted bounds in variable Lebesgue spaces

Abstract

In this paper we prove boundedness of Calderón-Zygmund operators and the Christ-Goldberg maximal operator in the matrix-weighted variable Lebesgue spaces recently introduced by Cruz-Uribe and the second author. Our main tool to prove these bounds is through bounding a Goldberg auxiliary maximal operator. As an application, we obtain a quantitative extrapolation theorem for matrix-weighted variable Lebesgue spaces from the recent framework of directional Banach function spaces of the first author.

32 pages, final version, accepted for publication in Ann. Fenn. Math