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Weighted Dunkl transform inequalities and application on radial Besov spaces
- Source :
- ANNALI DELL'UNIVERSITA' DI FERRARA. 59:199-220
- Publication Year :
- 2013
- Publisher :
- Springer Science and Business Media LLC, 2013.
-
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.
- 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
Subjects
Details
- ISSN :
- 18271510 and 04303202
- Volume :
- 59
- Database :
- OpenAIRE
- Journal :
- ANNALI DELL'UNIVERSITA' DI FERRARA
- Accession number :
- edsair.doi...........1bf7d9597163d4e4ad322acae7d06cfe