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Boundedness and continuity of Marcinkiewicz integrals associated to homogeneous mappings on Triebel-Lizorkin spaces |
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| Authors: | Feng LIU Zunwei FU Seong Tae JHANG |
| Affiliation: | 1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China2. Department of Mathematics, Linyi University, Linyi 276005, China3. School of Mathematical Sciences, Qufu Normal University, Qufu 273100, China4. Department of Computer Science, The University of Suwon, Wau-ri, Bongdam-eup, Hwaseong-si, Gyeonggi-do, 445-743, Korea |
| Abstract: | We establish the boundedness and continuity of parametric Marcinkiewicz integrals associated to homogeneous compound mappings on Triebel-Lizorkin spaces and Besov spaces. Here the integral kernels are provided with some rather weak size conditions on the unit sphere and in the radial direction. Some known results are naturally improved and extended to the rough case. |
| Keywords: | Parametric Marcinkiewicz integral homogeneous mapping Triebel-Lizorkin space Besov space |
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