Hardy Space Estimates for Littlewood-Paley-Stein Square Functions and Calderón-Zygmund Operators

2015/04/30 by Jarod Hart, Guozhen Lu, Hart, Jarod +1
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #math.CA #math.FA

paper · pdf · doi:10.48550/arxiv.1505.02185

To appear in the Journal of Fourier Analysis and Application

arxiv created 2015/04/30 · arxiv updated 2015/05/12

Abstract

In this work, we give new sufficient conditions for a Littlewood-Paley-Stein square function and necessary and sufficient conditions for a Calderón-Zygmund operator to be bounded on Hardy spaces H^p with indices smaller than 1. New Carleson measure type conditions are defined for Littlewood-Paley-Stein operators, and we show that they are sufficient for the associated square function to be bounded from H^p into L^p. New polynomial growth BMO conditions are also introduced for Calderón-Zygmund operators. These results are applied to prove that Bony paraproducts can be constructed such that they are bounded on Hardy spaces with exponents ranging all the way down to zero.

Related

• Weighted Norm Inequalities for Parametric Littlewood-Paley Operators
• Square function characterization of Hardy-type spaces
• Boundedness of Bi-parameter Littlewood-Paley operators on product Hardy space
• Calderón-Zygmund operators on local hardy spaces
• Remarks on square functions in the Littlewood-Paley theory