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A Characterization of the Hardy Space Associated with the Dunkl Transform
- Source :
- Complex Analysis and Operator Theory. 15
- Publication Year :
- 2021
- Publisher :
- Springer Science and Business Media LLC, 2021.
-
Abstract
- For $$p\ge p_0:=2\lambda /(2\lambda +1)$$ with $$\lambda >0$$ , the Hardy space $$H_\lambda ^p({\mathbb {R}}^2_+)$$ associated with the Dunkl transform $${\mathscr {F}}_{\lambda }$$ and the Dunkl operator D on the line $${\mathbb {R}}$$ , where $$(D_xf)(x)=f'(x)+\frac{\lambda }{x} (f(x)-f(-x))$$ , is the set of functions $$F=u+iv$$ on the half plane $${\mathbb {R}}^2_+=\{(x,y):\,x\in {\mathbb {R}}, y>0\}$$ , satisfying the generalized Cauchy–Riemann equations $$D_xu-\partial _yv=0$$ , $$\partial _yu+D_xv=0$$ , and $$\sup _{y>0}\int _{{\mathbb {R}}}| F(x,y)|^p|x|^{2\lambda }dx
- Subjects :
- Riesz potential
Applied Mathematics
010102 general mathematics
Boundary (topology)
Characterization (mathematics)
Operator theory
Hardy space
Type (model theory)
Lambda
01 natural sciences
Combinatorics
Computational Mathematics
symbols.namesake
Computational Theory and Mathematics
0103 physical sciences
symbols
010307 mathematical physics
0101 mathematics
Dunkl operator
Mathematics
Subjects
Details
- ISSN :
- 16618262 and 16618254
- Volume :
- 15
- Database :
- OpenAIRE
- Journal :
- Complex Analysis and Operator Theory
- Accession number :
- edsair.doi...........ea4d411426571b7e5081ab636bea55fe