Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 44, 2019, 459-484

WEIGHTED COMPLETE CONTINUITY FOR THE COMMUTATOR OF MARCINKIEWICZ INTEGRAL

Guoen Hu

Beijing Normal University Zhuhai, School of Applied Mathematics
Zhuhai 519087, P.R. China; guoenxx 'at' 163.com

Abstract. Let Ω be homogeneous of degree zero, have mean value zero and integrable on the unit sphere, and M_Ω be the higher-dimensional Marcinkiewicz integral associated with Ω. In this paper, the author considers the complete continuity on weighted L^p(Rⁿ) spaces with A_p(Rⁿ) weights, weighted Morrey spaces with A_p(Rⁿ) weights, for the commutator generated by CMO(Rⁿ) functions and M_Ω when Ω satisfies certain size conditions.

2010 Mathematics Subject Classification: Primary 42B25; Secondary 47B07.

Key words: Commutator, Marcinkiewicz integral, completely continuous operator, Fourier transform, weighted Morrey space.

Reference to this article: G. Hu: Weighted complete continuity for the commutator of Marcinkiewicz integral. Ann. Acad. Sci. Fenn. Math. 44 (2019), 459-484.

Full document as PDF file

https://doi.org/10.5186/aasfm.2019.4428