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Hardy inequalities for the fractional powers of the Grushin operator

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    * Corresponding author

M. Song is supported by the China Postdoctoral Science Foundation (Grant No. 2017M623230), the National Natural Science Foundation of China (Grant No. 11701452), the Natural Science Foundation of Shaanxi Province (Grant No. 2020JQ-112) and the Fundamental Research Funds for the Central Universities (Grant No. 3102018zy041). J. Tan is partially supported by Chile Government grant FONDECYT grant 1160519 and by MINECO grants MTM2014-52402-C3-1-P and MTM2017-84214-C2-1-P (Spain Government Grants)

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  • We establish uncertainty principles and Hardy inequalities for the fractional Grushin operator, which are reduced to those inequalities for the fractional generalized sublaplacian. The key ingredients to obtain them are an explicit integral representation and a ground state representation for the fractional powers of generalized sublaplacian.

    Mathematics Subject Classification: Primary: 35H20, 26D10.

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