Abstract
For and , let be the fractional differential operator and be the singular integral operator. We obtain a necessary and sufficient condition on the function to guarantee that is a bounded operator on a function space such as and for any . Furthermore, we establish a necessary and sufficient condition on the function to guarantee that is a bounded operator from to and from to . This is a new theory. Finally, we apply our general theory to the Hilbert and Riesz transforms.
Citation
Yanping Chen. Yong Ding. Guixiang Hong. "Commutators with fractional differentiation and new characterizations of BMO-Sobolev spaces." Anal. PDE 9 (6) 1497 - 1522, 2016. https://doi.org/10.2140/apde.2016.9.1497
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