Singular and fractional integral operators with variable kernels on the weak Hardy spaces. (English) Zbl 1321.42034

Wang, Hua

Commun. Math. Anal. 18, No. 1, 48-63 (2015).

Summary: In this paper, by using the decomposition theorem for weak Hardy spaces, we will obtain the boundedness properties of some integral operators with variable kernels on these spaces, under some Dini type conditions imposed on the variable kernel \(\Omega(x,z)\).

MSC:

42B20	Singular and oscillatory integrals (Calderón-Zygmund, etc.)
42B30	\(H^p\)-spaces
42B35	Function spaces arising in harmonic analysis

Keywords:

singular integral operators; fractional integral operators; variable kernels; weak Hardy spaces; atomic decomposition