Commentary on Two Papers of A. P. Calderón

For n + 1 = 2, these results had been established earlier by Plessner (1923) and by Marcinkiewicz and Zygmund (1938), who exploited the connection with holomorphic functions and mappings, including the conformal invariance of ∫ |f ′|2 for holomorphic f , and properties of conformal mappings of domains bounded by rectifiable curves. Concerning his motivation, Calderón discloses only that he aims to give a new proof that generalizes to functions of several variables, and that the topic was proposed by Antoni Zygmund. These two theorems, and elements of their proofs, have been prototypes for subsequent refinements and extensions at the hands of other authors. They have exerted