Abstract
We consider the Duhamel equation ? ? f = g in the subspace C? xy = {f ? C? ([0, 1] ? [0, 1]) : f (x, y) = F (xy) for some F ? C? [0, 1] of the space C? ([0, 1] ? [0, 1]) and prove that if ? pxy=0, 0, then this equation is uniquely solvable in C? x y. The commutant of the restricted double integration operator Wxy f (xy) := ?x 0 ?y 0 f (t?) d?dt on C? x y is also described. Some other related questions are also discussed.
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