ESTIMATES FOR THE MAXIMAL SINGULAR INTEGRALS WITHOUT DOUBLING CONDITION

摘要

It is shown that the maximal singular integral operator with kernels satisfying Hoe rmander's condition is of weak type (1,1) and L~p(1 < p < ∞) bounded without assuming that the underlying measure μ is doubling. Under stronger smoothness conditions,such estimates can be obtained by using a Cotlar's inequality. This inequality is not applicable here and it is noticeable that the Cotlar's inequality maybe fails under Hoermander's condition.