Sparse domination via the helicoidal method

Using exclusively the localized estimates upon which helicoidal method was built by authors, we show how sparse can also be obtained. This approach yields a domination for scalar and multiple vector-valued extensions of operators alike. We illustrate these ideas an $n$-linear Fourier multiplier whose symbol is singular along $k$-dimensional subspace $\Gamma={\xi\_1+\cdots+\xi\_{n+1}=0}$, where $k < (n+1)/{2}$, variational Carleson operator.