Commutators of Marcinkiewicz integrals with rough kernels on Herz-type Hardy spaces with variable exponent

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 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

Commutators of integral operators with variable kernels on Hardy spaces

Abstract. Let TΩ,α (0 ≤ α < n) be the singular and fractional integrals with variable kernel Ω(x,z), and [b,TΩ,α ] be the commutator generated by TΩ,α and a Lipschitz function b. In this paper, the authors study the boundedness of [b,TΩ,α ] on the Hardy spaces, under some assumptions such as the Lr-Dini condition. Similar results and the weak type estimates at the end-point cases are also given...

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

The Wavelet Characterization of Herz-type Hardy Spaces with Variable Exponent

In this paper, using the atomic theory of the Herz-type Hardy spaces with variable exponent, we give their wavelet characterization by means of some discrete tent spaces with variable exponent at the origin.