Polynomial tractability for integration in an unweighted function space with absolutely convergent Fourier series

In this note, we prove that the following function space with absolutely convergent Fourier series \[ F_d≔\left \{ f\in L^2([0,1)^d)\middle | \|f\|≔\sum _{\boldsymbol {k}\in {\mathbb {Z}}^d}|\hat {f}({\boldsymbol {k}}) |\max \left (1,\min _{j\in \operatorname {supp}({\boldsymbol {k}})}\log |k_j|\right )