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Abstract
Let X be a metric space with a doubling measure and let L be a linear operator in L^{2} (X) which generates a semigroup e ^{}^{t}^{L} whose kernels p_{t}(x, y) , t > 0 , satisfy the Gaussian upper bound. In this article, we prove sharp L _{w}^{p} norm inequalities for a number of square functions associated to L including the vertical square functions, the Lusin area integral square functions and the Littlewood–Paley gfunctions. We note that our conditions on the heat kernels p_{t} (x, y) are mild in the sense that the associated kernels of the square functions do not possess enough regularity for those operators to belong to the standard class of Calderón–Zygmund operators.
Original language  English 

Pages (fromto)  874900 
Number of pages  27 
Journal  Journal of Geometric Analysis 
Volume  30 
Issue number  1 
Early online date  4 Mar 2019 
DOIs  
Publication status  Published  Jan 2020 
Keywords
 Heat kernel
 Square function
 Sharp weighted estimate
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Projects
 1 Active

Harmonic analysis: function spaces and partial differential equations
Duong, X., Hofmann, S., Ouhabaz, E. M. & Wick, B.
11/02/19 → 10/02/22
Project: Other