We give a structure theorem for Boolean functions on the biased hypercube which are $\epsilon$-close to degree $d$ in $L_2$, showing that they are close to sparse juntas. Our structure theorem implies that such functions are $O(\epsilon^{C_d} + p)$-close to constant functions. We pinpoint the exact value of the constant $C_d$.

翻译：我们给出了偏置超立方体上在$L_2$中与$d$次多项式$\epsilon$-接近的布尔函数的一个结构定理，表明它们接近稀疏朱塔。该结构定理推断，此类函数与常数函数接近到$O(\epsilon^{C_d} + p)$。我们精确确定了常数$C_d$的值。