discrete Hausdorff-Young inequality

Question

I am consider inequality about hausdorff young inequality on group,the group is $\mathbb{Z}(n)$,we know Hausdorff Young inequality such like $ \left\|f_1*f_2\right\|_r\leq C\left\|f_1\right\|_{q_1} \left\|f_2\right\|_{q_2}$,at first ,I suppose $f_1(0)=1,f_1(1)=k_1,f_2(0)=1,f_2(1)=k_2$,we use the convolution on $\mathbb{Z}_2$,so $f_1*f_2(0)=\frac{1}{2}(1+k_1k_2),f_1*f_2(1)=\frac{1}{2}(k_1+k_2)$, now i want to proof $\frac{1}{2}((1+k_1k_2)^p+(k_1+k_2)^p)^{\frac{1}{p}}\leq C(1+k_1^{r_1})^{\frac{1}{r_1}}(1+k_2^{r_2})^{\frac{1}{r_2}}$,$\sum_1^2\frac{1}{r_i}=2-\frac{1}{p^{'}}, 1\leq r_1,r_2,p<\infty$ can you help me? Thank you very much.