Abstract
In this paper, we obtain a characterization of \(H^{p}_{\varDelta _{\nu }}({\mathbb {R}}^{n}_{+})\) Hardy spaces by using atoms associated with the radial maximal function, the nontangential maximal function and the grand maximal function related to \(\varDelta _{\nu }\) Laplace–Bessel operator for \(\nu >0\) and \(1<p<\infty \). As an application, we further establish an atomic characterization of Hardy spaces \(H^{p}_{\varDelta _{\nu }}({\mathbb {R}}^{n}_{+})\) in terms of the high order Riesz–Bessel transform for \(0<p\le 1\).
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Acknowledgements
The research of V.S. Guliyev was partially supported by the Grant of the \(1\hbox {st}\) Azerbaijan–Russia Joint Grant Competition (Agreement Number No. EIF-BGM-4-RFTF-1/201721/01/1) and by the Ministry of Education and Science of the Russian Federation (Agreement Number No. 02.a03.21.0008).
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Keskin, C., Ekincioglu, I. & Guliyev, V.S. Characterizations of Hardy spaces associated with Laplace–Bessel operators. Anal.Math.Phys. 9, 2281–2310 (2019). https://doi.org/10.1007/s13324-019-00335-5
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DOI: https://doi.org/10.1007/s13324-019-00335-5
Keywords
- Atomic decomposition
- Fourier–Bessel transform
- Generalized shift operator
- Hardy space
- Riesz–Bessel transform