ABSTRACT
The Hardy transform was first discussed by the great English mathematician G.H. Hardy in 1925 in a paper https://www.w3.org/1998/Math/MathML"> [ 90 ] https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780138752859/46b98bf4-f43d-4c1b-bad9-d831e2ef6414/content/eq6514.tif" xmlns:xlink="https://www.w3.org/1999/xlink"/> in which he was interested in simplifying the proof of a formula involving Bessel functions that was proved earlier by Titchmarsh. Hardy introduced an integral transform, which is now called the Hardy transform, and reported on its inversion formula, but provided no proofs for it. It was R. Cooke [46] who established the validity of Hardy's inversion formula, together with another inversion formula by Titchmarsh.
