Fractional Adams-Moser-Trudinger type inequality on Heisenberg group

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dc.contributor.author Gupta, Madhu
dc.contributor.author Tyagi, Jagmohan
dc.date.accessioned 2020-02-22T06:10:44Z
dc.date.available 2020-02-22T06:10:44Z
dc.date.issued 2020-06
dc.identifier.citation Gupta, Madhu and Tyagi, Jagmohan, "Fractional Adams-Moser-Trudinger type inequality on Heisenberg group", Nonlinear Analysis, DOI: 10.1016/j.na.2020.111747, vol. 195, Jun. 2020. en_US
dc.identifier.issn 1392-5113
dc.identifier.uri https://doi.org/10.1016/j.na.2020.111747
dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/5098
dc.description.abstract The aim of this paper is to establish singular fractional Adams–Moser–Trudinger inequality for both bounded and unbounded domains in the Heisenberg group We first establish fractional Adams–Moser–Trudinger type inequality on domain with finite measure (Theorem 1.12) and then using this inequality and Hardy–Littlewood–Sobolev inequality adapted to the result of R. O’Neil (1963), we establish singular fractional Adams–Moser–Trudinger type inequality on domain with finite measure (Theorem 1.13). We also establish singular fractional Adams–Moser–Trudinger type inequality in using the approach of N. Lam and G. Lu (2012, 2013). The main idea of our approach is that any function in higher order fractional Sobolev space in Heisenberg group can be represented in terms of Riesz potential and then using techniques from harmonic analysis and kernel properties of the associated operator, we establish fractional Adams–Moser–Trudinger type inequality in In this paper, our approach is quite simple and free from symmetrization arguments. As an applications of our theorems, we establish the existence of solution to the following class of problems
dc.description.statementofresponsibility by Madhu Gupta and Jagmohan Tyagi
dc.format.extent vol. 195
dc.language.iso en_US en_US
dc.publisher Institute of Mathematics and Informatics en_US
dc.subject Variational methods
dc.subject Fractional Adams–Moser–Trudinger inequality
dc.subject Heisenberg group
dc.subject Finite measure
dc.subject Sobolev space
dc.title Fractional Adams-Moser-Trudinger type inequality on Heisenberg group en_US
dc.type Article en_US
dc.relation.journal Nonlinear Analysis


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