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Abstract
Let L be a nonnegative selfadjoint operator on L^{2}(X) where X is a metric space with a doubling measure. Assume that the kernels of the semigroup generated by − L satisfy a suitable upper bound related to a critical function ρ but these kernels are not assumed to satisfy any regularity conditions on spacial variables. In this paper, we prove the quantitative weighted estimates for some square functions associated to L which include the vertical square function, the conical square function and the gfunctions. The novelty of our results is that the square functions associated to L might have rough kernels, hence do not belong to the CalderónZygmund class, and the class of weights is larger than the class of Muckenhoupt weights. Our results have applications in various settings of Schrödinger operators such as magnetic Schrödinger operators on the Euclidean space ℝ^{n} and Schrödinger operators on doubling manifolds.
Original language  English 

Pages (fromto)  545569 
Number of pages  25 
Journal  Potential Analysis 
Volume  57 
Issue number  4 
Early online date  27 May 2021 
DOIs  
Publication status  Published  Dec 2022 
Keywords
 Critical function
 Quatitative weighted estimate
 Square function
 Heat kernel
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Dive into the research topics of 'Quantitative estimates for square functions with new class of weights'. Together they form a unique fingerprint.Projects
 1 Finished

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