A new look at subrepresentation formulas
Abstract
We extend the subrepresentation formula |f(x)| cn\,I1(|∇ f|)(x) in several ways. First, we consider more general A1-potential operators on the right-hand side and prove local and global pointwise inequalities for these operators. Second, we show that we can improve the right-hand side using fractional derivatives. Finally, we extend our results to rough singular integral operators, similar to the main result in [HMP1].
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