Fractional type Marcinkiewicz integral operators on function spaces

Abstract

Abstract In this paper, we discussed about the boundedness of the fractional type Marcinkiewicz integral operators, and improved a result given by Chen, Fan and Ying in 2002. They showed that under certain conditions the fractional type Marcinkiewicz integral operators are bounded from the Triebel–Lizorkin spaces F ˙ p q α ( ℝ n ) ${\dot{F}_{pq}^{\alpha }({\mathbb {R}^n})}$ to L p ( ℝ n ) ${L^p({\mathbb {R}^n})}$ . We greatly weakened their assumptions and extended their results to a pretty much more general way.