Maximal Riesz transform in terms of Riesz transform on quantum tori and Euclidean space

Xudong Lai, Xiao Xiong, Yue Zhang

For $1<p<\infty$, we establish the $L_p$ boundedness of the maximal Riesz transforms in terms of the Riesz transforms on quantum tori $L_p({\mathbb{T}}_{\hat{I}}^d¸)$, and quantum Eucl…