Riesz transforms, fractional power and functional calculus of Schr?dinger operators on weighted -spaces

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• 作者：Joyce Assaad ^{joyce.assaad@ndu.edu.lb joyceassaad67@yahoo.fr}
• 关键词：Riesz transforms ; Schr&ouml ; dinger operators ; Fractional powers ; Functional calculus ; Off-diagonal estimates ; Muckenhoupt class ; Reverse H&ouml ; lder class
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2013
• 出版时间：1 June, 2013
• 年：2013
• 卷：402
• 期：1
• 页码：220-233
• 全文大小：484 K

文摘

We consider the Schr?dinger operator on where , and is a weight in some Muckenhoupt class. We study the boundedness of Riesz transform type operators and on . Our result extends the one of Bui (2010)? to signed potentials and treat the case where . It also gives a weighted version of our earlier results Assaad (2011)?, Assaad and Ouhabaz (2012)? and of the result (Auscher and Ben Ali 2007)? to weighted Lebesgue spaces. We study also the boundedness from to of the fractional power and the -boundedness of the -functional calculus of .