Marcinkiewicz Functions along Flat Surfaces with Hardy Space Kernels

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 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...

Flat surfaces in the hyperbolic 3-space

In this paper we give a conformal representation of flat surfaces in the hyperbolic 3space using the complex structure induced by its second fundamental form. We also study some examples and the behaviour at infinity of complete flat ends. Mathematics Subject Classification (1991): 53A35, 53C42