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Sobolev-type spaces on the dual of the Chébli-Trimèche hypergroup and applications. (English) Zbl 1470.42045

Summary: We define and study Sobolev-type spaces \(W_A^{s, p} \left(\mathbb{R}_+\right)\) associated with singular second-order differential operator on \(\left(0, \infty\right)\). Some properties are given; in particular we establish a compactness-type imbedding result which allows a Reillich-type theorem. Next, we introduce a generalized Weierstrass transform and, using the theory of reproducing kernels, some applications are given.

MSC:

42B35 Function spaces arising in harmonic analysis
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