Abstract—In this study, the Flett potential spaces are defined and a characterization of these potential spaces is given. Most of the known characterizations of classical potential spaces such as Riesz, Bessel potentials spaces and their generalizations are given in terms of finite differences. Here, by taking wavelet measure instead of finite differences, a weighted wavelet-like transform associated with Poisson semigroup is defined. And, by making use of this weighted wavelet-like transform, a new “truncated" integrals are defined, then using these integrals a characterization of the Flett potential spaces is given.

Index Terms—Fractional integrals, weighted wavelet-like transform, flett potential spaces.

Sinem Sezer Evcan, Sevda Barut are with Akdeniz University, Faculty of Education, 07058, Antalya, Turkey.

Cite:Sinem Sezer Evcan, Sevda Barut, "Flett Potential Spaces and a Weighted Wavelet-Like Transform," International Journal of Applied Physics and Mathematics vol. 10, no. 3, pp. 112-122, 2020.

Copyright © 2020 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).