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Riesz Transforms Associated With Heisenberg Groups And Grushin Operators

Electronic Theses of Indian Institute of Science

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Title Riesz Transforms Associated With Heisenberg Groups And Grushin Operators
 
Creator Sanjay, P K
 
Subject Riesz Transforms
Heisenberg Groups
Grushin Operators
Differential Operators
Heisenberg Group
Hermite Polynomials
Hermite Functions
Laguerre Functions
Hermite Expansion
Laguerre Expansion
Mathematics
 
Description We characterise the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order Riesz transforms associated to the Hermite operator. Using transference theorems, we deduce boundedness theorems for Riesz transforms on the reduced Heisenberg group and hence also for the Riesz transforms associated to special Hermite and Laguerre expansions.
Next we study the Riesz transforms associated to the Grushin operator G = - Δ - |x|2@t2 on Rn+1. We prove that both the first order and higher order Riesz transforms are bounded on Lp(Rn+1): We also prove that norms of the first order Riesz transforms are independent of the dimension n.
 
Contributor Thangavelu, Sundaram
 
Date 2015-12-08T10:07:31Z
2015-12-08T10:07:31Z
2015-12-08
2012-07
 
Type Thesis
 
Identifier http://etd.iisc.ernet.in/handle/2005/2496
http://etd.ncsi.iisc.ernet.in/abstracts/3223/G25451-Abs.pdf
 
Language en_US
 
Relation G25451