Boundedness of higher-order Marcinkiewicz-Type integrals

Boundedness of higher-order Marcinkiewicz-Type integrals

Let A be a function with derivatives of order m and DγA∈ Λ̇β (0 < β < 1, |γ| =m). The authors in the paper proved that ifΩ∈ Ls(Sn−1) (s≥ n/(n−β)) is homogeneous of degree zero and satisfies a vanishing condition, then both the higher-order Marcinkiewicz-type integral μΩ and its variation μ̃ A Ω are bounded from L p(Rn) to Lq(Rn) and from L1(Rn) to Ln/(n−β),∞(Rn), where 1 < p < n/β and 1/q = 1/p− ...

Boundedness of Marcinkiewicz integrals with mixed homogeneity along compound surfaces

*Correspondence: [email protected] 1School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China Full list of author information is available at the end of the article Abstract In this note we establish the Lp boundedness of Marcinkiewicz integrals with mixed homogeneity along compound surfaces, which improve and extend some previous results. The main ingredient is to presen...

Boundedness of Marcinkiewicz Integrals with Rough Kernel on the Herz-Type Spaces

In this note, it is proved that the Marcinkiewicz integral with rough kernel defined by

Boundedness of Marcinkiewicz integrals with rough kernels on Musielak-Orlicz Hardy spaces

Let [Formula: see text] satisfy that [Formula: see text], for any given [Formula: see text], is an Orlicz function and [Formula: see text] is a Muckenhoupt [Formula: see text] weight uniformly in [Formula: see text]. The Musielak-Orlicz Hardy space [Formula: see text] is defined to be the set of all tempered distributions such that their grand maximal functions belong to the Musielak-Orlicz spa...

Boundedness on Hardy-Sobolev Spaces for Hypersingular Marcinkiewicz Integrals with Variable Kernels