Rough singular integrals on Triebel–Lizorkin space and Besov space |
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| Authors: | Yanping Chen Yong Ding |
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| Affiliation: | aDepartment of Mathematics and Mechanics, Applied Science School, University of Science and Technology Beijing, Beijing 100083, People's Republic of China;bSchool of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems (BNU), Ministry of Education, Beijing 100875, People's Republic of China |
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| Abstract: | In this paper the authors prove that the homogeneous singular integral TΩ with Ω H1(Sn−1) is bounded on the Triebel–Lizorkin spaces and the Besov spaces. These results answer an open problem proposed by Chen and Zhang in [J. Chen, C. Zhang, Boundedness of rough singular integral on the Triebel–Lizorkin spaces, J. Math. Anal. Appl. 337 (2008) 1048–1052]. The same results hold also for the rough singular integral operators TΩ,h with radial function kernels. |
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| Keywords: | Rough singular integral Hardy space kernel Triebel– Lizorkin space Besov space |
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