Let f (x) and K (x) be two functions integrable over the interval (-∞,+∞). It is very well known that their composition ∫_ - ∞ ^ + ∞ f(t)K( x - t )dt exists, as an absolutely convergent integral, for almost every x. The integral can, however, exist almost everywhere even if K is not absolutely integrable. The mostinteresting special case is that of K (x) = 1/x. Let us set f̃(x) = 1/π ∫_ - ∞ ^ + ∞ f(t)x - tdt .
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Calderón et al. (1952) studied this question.