  In this paper we show sharp lower bounds for norms of even homogeneous
Fourier multipliers in $\mathcal L(L^p(\mathbb R^d; X))$ for $1<p<\infty$ and
for a UMD Banach space $X$ in terms of the range of the corresponding symbol.
For example, if the range contains $a_1,\ldots,a_N \in \mathbb C$, then the
norm of the multiplier exceeds $\|a_1R_1^2 + \cdots + a_NR_N^2\|_{\mathcal
L(L^p(\mathbb R^N; X))}$, where $R_n$ is the corresponding Riesz transform. We
also provide sharp upper bounds of norms of Ba\~{n}uelos-Bogdan type
multipliers in terms of the range of the functions involved. The main tools
that we exploit are $A$-weak differential subordination of martingales and
UMD$_p^A$ constants, which are introduced here.
