A new characterization of the Riesz potential spaces with the aid of a composite wavelet transform

作者：Sezer Sinem; Aliev Ilham A^*

来源：Journal of Mathematical Analysis and Applications, 2010, 372(2): 549-558.

DOI：10.1016/j.jmaa.2010.07.009

• Fractional integrals
• Riesz potentials
• Wavelet transform
• Semigroup
• Riesz potential spaces
• Inversion formulas

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.

• 出版日期2010-12-15