L p ( μ ) → L q ( ν ) Characterization for Well Localized Operators

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Vuorinen , E 2016 , ' L p ( μ ) → L q ( ν ) Characterization for Well Localized Operators ' , Journal of Fourier Analysis and Applications , vol. 22 , no. 5 , 10.1007/s00041-015-9453-7 , pp. 1059-1075 . https://doi.org/10.1007/s00041-015-9453-7

Title: L p ( μ ) → L q ( ν ) Characterization for Well Localized Operators
Author: Vuorinen, Emil
Contributor: University of Helsinki, Department of Mathematics and Statistics
Date: 2016-10
Language: eng
Number of pages: 17
Belongs to series: Journal of Fourier Analysis and Applications
ISSN: 1069-5869
URI: http://hdl.handle.net/10138/174044
Abstract: We consider a two weight L-p(mu) -> L-q(nu) -inequality for well localized operators as defined and studied by Nazarov et al. (Math Res Lett 15(3):583-597, 2008) when . A counterexample of Nazarov shows that the direct analogue of the results in Nazarov et al. (Math Res Lett 15(3):583-597, 2008) fails for . Here a new square function testing condition is introduced and applied to characterize the two weight norm inequality. The use of the square function testing condition is also demonstrated in connection with certain positive dyadic operators.
Subject: 111 Mathematics
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