Is there any Integral transform whose kernel is logarithmic function ?

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Luisiana Cundin

Hello, yes there is...it is Cauchy's integral. See attached paper for further details.

Article Stieltjes Integral Theorem and The Hilbert Transform

Vikash Pandey

I guess, you coming from fractional calculus studies. Yes, logarithm kernel is very much included in the definition of Riesz potential and the kernel is called Riesz kernel. See attached screenshot from Samko, Kilbas book.

Rahmatullah Ibrahim Nuruddeen

Have you played with the Mellin transform kernel before? I guess you would get it...