 The sharp function can be used to obtain a point-wise inequality regarding singular integrals.Suppose we have an operator "T" which is bounded on "L2"(R"n"), so we have

for all smooth and compactly supported "f".Suppose also that we can realize "T" as convolution against a kernel "K" in the sense that, whenever "f" and "g" are smooth and have disjoint support

Finally we assume a size and smoothness condition on the kernel "K"