ON THE SUPERPOSITION OPERATOR BETWEEN SOBOLEV SPACES: WELL-DEFINEDNESS, CONTINUITY, BOUNDEDNESS, AND HIGHER-ORDER CHAIN RULE

摘要

This paper deals with the study of superposition operators between two arbitrary Sobolev spaces. The sufficient conditions which ensure the well-definedness, the continuity, the boundedness, and the validity of the higher-order chain rule for such operators, obtained in the previous papers [8, 9], are heuristically analyzed. This point of view may be a start point in the attempt to prove that these sufficient conditions are necessary as well.