If you want to use your display name, you cannot use LookupId="TRUE"or Type="User". It should be:
<Contains>
<FieldRef Name="CreatedBy" />
<Value Type="Text">Smith</Value>
</Contains>
See my answer here for more details .
Edit:
, , <And></And> node -. , , - :
<Where>
<And>
<And>
<Leq>
<FieldRef Name="Created" />
<Value Type="DateTime" IncludeTimeValue="FALSE">2011-1-8</Value>
</Leq>
<Geq>
<FieldRef Name="Created" />
<Value Type="DateTime" IncludeTimeValue="FALSE">2011-1-2</Value>
</Geq>
</And>
<Contains>
<FieldRef Name="CreatedBy" />
<Value Type="Text">Smith</Value>
</Contains>
</And>
</Where>