Study the help pages for these functions until you think you understand it
And test it carefully before you depend on it.
Method 1:
In[1]:= ca = {-5, 2, 1, -4};
p = {4, 3, 0, 2};
f[{ca_, p_}] := If[Abs[ca] > p, Sign[ca], 0];
Map[f, Transpose[{ca, p}]]
Out[4]= {-1, 0, 1, -1}
Method 2. Perhaps more cryptic, but more in the usual Mathematica programming style.
In[5]:= ca = {-5, 2, 1, -4};
p = {4, 3, 0, 2}; Map[
If[Abs[#[[1]]] > #[[2]], Sign[#[[1]]], 0] &, Transpose[{ca, p}]]
Out[6]= {-1, 0, 1, -1}