In this paper, we show that Hilbert transforms along some curves are bounded on for some and some UMD spaces . In particular, we prove that Hilbert transforms along some curves are completely -bounded in the terminology from operator space theory. Moreover, we obtain the -boundedness of anisotropic singular integrals by using the “method of rotations” of Calderón–Zygmund. All these results extend preexisting related ones.
"Vector-valued Hilbert transforms along curves." Banach J. Math. Anal. 10 (2) 430 - 450, April 2016. https://doi.org/10.1215/17358787-3589397