Abstract
© 2018, Springer Science+Business Media, LLC, part of Springer Nature. We prove that the spherical mean value of the Dunkl-type generalized translation operator τ y is a positive L p -bounded generalized translation operator T t . As applications, we prove the Young inequality for a convolution defined by T t , the L p -boundedness of τ y on radial functions for p> 2 , the L p -boundedness of the Riesz potential for the Dunkl transform, and direct and inverse theorems of approximation theory in L p -spaces with the Dunkl weight.
Original language | English |
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Pages (from-to) | 555-605 |
Journal | Constructive Approximation |
Volume | 49 |
DOIs | |
Publication status | Published - 15 Jun 2019 |
Keywords
- Convolution
- Dunkl transform
- Generalized translation operator
- Riesz potential