Boundedness of Monge-Ampère singular integral operators on Besov spaces. (English) Zbl 1458.42013
In the first and the second part of this paper the authors give an introduction and preliminaries and historical remarks on Monge-Ampere singular integral operators with suitable theorems. In the third part of this paper they show the existence of the approximation to the identity with a suitable lemma.
In the fourth part and the fifth part of the paper they give a Calderón-type reproducing formula for \(B_{p,\mathcal F}^{\alpha,q} \) and its dual and a basic property of Besov spaces with suitable theorems. In the sixth part of the paper they give the boundedness on \(B_{p,\mathcal F}^{\alpha,q} \) with a suitable lemma. This paper was written in very well manner.
Reviewer: Yogesh Sharma (Sardarpura)
MSC:
| 42B20 | Singular and oscillatory integrals (Calderón-Zygmund, etc.) |
| 42B10 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
| 42B35 | Function spaces arising in harmonic analysis |
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