2017/02/13 by Sawyer, Eric T., Wang, Zipeng
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.1702.03870
We investigate one and two weight norm inequalities for product fractional integrals. We show that in the one weight case, most of the 1 parameter theory carries over to the 2 parameter setting. However, in the two weight case, apart from the trivial case of product weights, the rectangle characteristic never controls the operator norm without side conditions. The Stein-Weiss extension of the classical Hardy-Littlewood-Sobolev inequality carries over to the setting of 2 parameters with nonproduct power weights using a sandwiching technique.