Sezer S., Aliev İ., "A new characterization of the Riesz potential spaces with the aid of a composite wavelet transform", JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.372, pp.549-558, 2010
<p> <span style="color: rgb(51, 51, 51); font-family: arial, helvetica, sans-serif; font-size: 13px; line-height: 22px; background-color: rgb(248, 248, 248);">We introduce a composite wavelet-like transform generated by the so-called beta-semigroup and a wavelet measure. This wavelet-like transform enables one to obtain a new explicit inversion formula for the Riesz potentials and a new characterization of the Riesz potential spaces. The usage of the concept "beta-semigroup", which is a natural generalization of the well-known Gauss-Weierstrass and Poisson semigroups, enables one to minimize the number of conditions on wavelet measure, no matter how big the order of Riesz's potentials is. </span></p>