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Journal of Function Spaces
Volume 2017 (2017), Article ID 4340805, 10 pages
Research Article

Weak Estimates of Singular Integrals with Variable Kernel and Fractional Differentiation on Morrey-Herz Spaces

College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China

Correspondence should be addressed to Shuangping Tao

Received 9 October 2017; Accepted 12 December 2017; Published 31 December 2017

Academic Editor: Henryk Hudzik

Copyright © 2017 Yanqi Yang and Shuangping Tao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let be the singular integral operator with variable kernel defined by and let be the fractional differentiation operator. Let and be the adjoint of and the pseudoadjoint of , respectively. In this paper, the authors prove that and are bounded, respectively, from Morrey-Herz spaces to the weak Morrey-Herz spaces by using the spherical harmonic decomposition. Furthermore, several norm inequalities for the product and the pseudoproduct are also given.