The authors consider one-sided weighted classes of Muckenhoupt type and study the weighted weak norm inequalities for certain one-sided oscillatory singular integrals with smooth kernel.
One-sided oscillatory singular integral operators and are defined by
where is a real polynomial defined on , and is a one-sided Calderón-Zygmund kernel. The following theorem is the main result of the paper.
Let , the class of one-sided weights. Then there exists a constant depending on the degree of and such that
for all Schwartz functions .