Herz-type Spaces Research Articles

APPLICATIONS OF HERZ-TYPE TRIEBEL-LIZORKIN SPACES

In this paper, the authors first establish the connections between the Herz-type Triebel-Lizorkin spaces and the well-known Herz-type spaces; the authors then study the pointwise multipliers for the Herz-type Triebel-Lizorkin spaces and show that pseudo-differential operators are bounded on these spaces by using pointwise multipliers.

Boundedness of commutators of strongly singular convolution operators on Herz-type spaces

The author investigates the boundedness of the higher order commutator of strongly singular convolution operator, T m b , on Herz spaces _

Boundedness of vector-valued operators on weighted Herz spaces

In this paper, the authors establish the weighted weak and strong type norm inequalities in the set of weighted Herz-type spaces for a vector-valued analogue of the Hardy-Littlewood maximal operator; and using this, the authors obtain the weightd inequalies for a wide class of sublinear singular operators defined onRn which include the Calderon-Zygmund operators as special cases. The fractional versions of these results are also given.

BOUNDEDNESS OF COMMUTATORS OF FRACTIONAL INTEGRATION ON HERZ-TYPE SPACES

This paper establishes some strong type and weak type estimates for commutator [b, Il] on Herz-type spaces, where b∈BMO(R2) and Il is a fractional integration with 0 <l <n.

Boundedness of some sublinear operators in weighted Herz-type spaces

Boundedness of some sublinear operators in weighted Herz-type spaces

The continuity of commutators on Herz-type spaces.

The continuity of commutators on Herz-type spaces.

Hardy-Littlewood-Sobolev Theorems of Fractional Integration on Herz-Type Spaces and its Applications

AbstractIn this paper, the authors first establish the Hardy-Littlewood-Sobolev theorems of fractional integration on the Herz spaces and Herz-type Hardy spaces. Then the authors give some applications of these theorems to the Laplacian and wave equations.