2021/12/08 by Yang, Sibei, Yang, Zhenyu
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2112.04252
In this article, the authors establish a general (two-weight) boundedness criterion for a pair of functions, (F,f), on ℝn in the scale of weighted Lebesgue spaces, weighted Lorentz spaces, (Lorentz--)Morrey spaces, and variable Lebesgue spaces. As applications, the authors give a unified approach to prove the (two-weight) boundedness of Calderón--Zygmund operators, Littlewood--Paley g-functions, Lusin area functions, Littlewood--Paley g^∗λ-functions, and fractional integral operators, in the aforementioned function spaces. Moreover, via applying the above (two-weight) boundedness criterion, the authors further obtain the (two-weight) boundedness of Riesz transforms, Littlewood--Paley g-functions, and fractional integral operators associated with second-order divergence elliptic operators with complex bounded measurable coefficients on ℝn in the aforementioned function spaces.