If you want to filter data by user ID you need to set LookupId="TRUE" for Author field:
<Eq>
<FieldRef Name="Author" LookupId="TRUE" />
<Value Type="Integer">1</Value>
</Eq>
If you want to use multiple values for this field you should check IN Element. So your CAML should look like this:
<In>
<FieldRef Name="Author" LookupId="True" />
<Values>
<Value Type="Integer">1</Value>
<Value Type="Integer">2</Value>
<Value Type="Integer">3</Value>
</Values>
</In>