Boundedness of Marcinkiewicz integralwith rough kernel onTriebel-Lizorkin spaces

Chun-jie ZHANG, Fang-fang REN, Yu-huai ZHANG, Gui-lian GAO

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Front. Inform. Technol. Electron. Eng ›› 2015, Vol. 16 ›› Issue (8) : 654-657. DOI: 10.1631/FITEE.1500082

Boundedness of Marcinkiewicz integralwith rough kernel onTriebel-Lizorkin spaces

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Abstract

This paper is a continuation of our previous work (Zhang and Chen, 2010b). Following the same general steps of the proof there, we make essential improvement on our previous theorem by recalculating a key inequality. Our result shows that the Marcinkiewicz integral, with a bounded radial function in its kernel, is still bounded on the Triebel-Lizorkin space.

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Marcinkiewicz integral / Triebel-Lizorkin spaces

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Chun-jie ZHANG, Fang-fang REN, Yu-huai ZHANG, Gui-lian GAO. Boundedness of Marcinkiewicz integralwith rough kernel onTriebel-Lizorkin spaces. Front. Inform. Technol. Electron. Eng, 2015, 16(8): 654‒657 https://doi.org/10.1631/FITEE.1500082

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