Vector-valued $q$-variational inequalities for averaging operators and Hilbert transform
Classical Analysis and ODEs
2019-07-29 v1
Abstract
Recently, in \cite{GXHTM}, the authors established -boundedness of vector-valued -variational inequalities for averaging operators which take values in the Banach space satisfying martingale cotype property. In this paper, we prove that martingale cotype property is also necessary for the vector-valued -variational inequalities, which is a question left open. Moreover, we characterize UMD property and martingale cotype property in terms of vector valued -variational inequalities for Hilbert transform.
Cite
@article{arxiv.1907.11633,
title = {Vector-valued $q$-variational inequalities for averaging operators and Hilbert transform},
author = {Guixiang Hong and Wei Liu and Tao Ma},
journal= {arXiv preprint arXiv:1907.11633},
year = {2019}
}