We introduce two classes of real analytic functions W U on an interval. Starting with rational functions to construct functions in W we allow the application of three types of operations: addition, integration and multiplication by a polynomial with rational coe cients. In a similar way to construct functions in U we allow integration, addition and multiplication of functions already constructed in U and multiplication by rational numbers. Thus, U is a subring of the ring of Pfa an functions Kh]. Two lower bounds on L 1-norm are proved on a function f from W (or from U, respectively) in terms of the complexity of constructing f.