Characterization of the boundedness of the segment multiplier on weighted Lebesgue spaces

Abstract

For $1<p<\infty$, we characterize the boundedness of the segment multiplier on $L^p(w)$ by a large-scale Muckenhoupt condition, obtained by restricting the classical $A_p$ condition to intervals of length at least one. The proof uses a discretization involving the discrete Hilbert transform on an associated weighted sequence space.

arXiv comment17 pages