Search

The inversion of Riesz potentials for Dunkl transform when G=Z2d is given by using the generalized wavelet transforms. It is also proved that the Riesz potentials Iακ are automorphisms on the Semyanistyi-Lizorkin spaces. [ABSTRACT FROM AUTHOR]

The smoothness of functions defined on (−1, 1) is characterized by the Poisson integrals of their Jacobi expansions. The generalized translation T and the generalized difference $${\widetilde{T}_t}$$ associated with the product formulas of Jacobi polynomials are used to illustrate the smoothness of functions, which leads to very natural generalizations of the classical results of Hardy-Littlewoood and Zygmund. [ABSTRACT FROM AUTHOR]