Analytic holonomicity of real C^ᵣj-class distributions

We introduce a notion of distributions on R n R^n, called distributions of C e x p C^ {exp} -class, based on wavelet transforms of distributions and the theory of Cluckers, Comte, Miller, Rolin, and Servi Duke Math. J. 167 (2018), pp. 1239–1309 about C e x p C^ {exp} -class functions. We prove that the framework of C e x p C^ {exp} -class distributions is closed under natural operations, like push-forward, pull-back, derivation and anti-derivation, and, in the tempered case, Fourier transforms. Our main result is the (real analytic) holonomicity of all distributions of C e x p C^ {exp} -class.