An integral estimate of Bessel function and its application

In this paper the authors give a new integral estimate of the Bessel function, which is an extension of Calderón-Zygmund’s result. As an application of this result, we prove that the parameterized Marcinkiewicz integral μ_Ω ^ρ with variable kernels is of type (2, 2), where the kernel function Θ does not have any smoothness on the unit sphere in ℝ ⁿ . This work was supported by the National Natural Science Foundation of China (Grant No. 10571015) and the Specialized Research Foundation for Doctor Programme (Grant No. 20050027025)