Weighted inequalities for product fractional integrals Academic Article uri icon

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abstract

  • 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.