Marcinkiewicz functions with Hardy space kernels

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

Hardy space of operator-valued analytic functions

We are concerned with Hardy and BMO spaces of operator-valued functions analytic in the unit disk of C. In the case of the Hardy space, we involve the atomic decomposition since the usual argument in the scalar setting is not suitable. Several properties (the Garsia-norm equivalent theorem, Carleson measure, and so on) of BMOA spaces are extended to the operator-valued setting. Then, the operat...

Boundedness for Multilinear Marcinkiewicz Operators on Certain Hardy Spaces

The boundedness for the multilinear Marcinkiewicz operators on certain Hardy and Herz-Hardy spaces are obtained.

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...