1. Weighted Dunkl transform inequalities and application on radial Besov spaces
- Author
-
Chokri Abdelkefi and Abdessattar Jemai
- Subjects
Mathematics::Functional Analysis ,Pure mathematics ,General Mathematics ,Numerical analysis ,Mathematical analysis ,Mathematics::Classical Analysis and ODEs ,Algebraic geometry ,Characterization (mathematics) ,symbols.namesake ,Operator (computer programming) ,Fourier analysis ,symbols ,Hardy's inequality ,Mathematics ,Dunkl operator - Abstract
In Dunkl theory on \(\mathbb R ^d\) which generalizes classical Fourier analysis, we prove first weighted inequalities for certain Hardy-type averaging operators. In particular, we deduce for specific choices of the weights the \(d\)-dimensional Hardy inequalities whose constants are sharp and independent of \(d\). Second, we use the weight characterization of the Hardy operator to prove weighted Dunkl transform inequalities. As consequence, we obtain Pitt’s inequality which gives an integrability theorem for this transform on radial Besov spaces.
- Published
- 2013