Carleson Measure and Tent Spaces on the Siegel Upper Half Space

Kai Zhao

doi:10.1155/2012/583156

Abstract

The Hausdorff capacity on the Heisenberg group is introduced. The Choquet integrals with respect to the Hausdorff capacity on the Heisenberg group are defined. Then the fractional Carleson measures on the Siegel upper half space are discussed. Some characterized results and the dual of the fractional Carleson measures on the Siegel upper half space are studied. Therefore, the tent spaces on the Siegel upper half space in terms of the Choquet integrals are introduced and investigated. The atomic decomposition and the dual spaces of the tent spaces are obtained at the last.

Highlights

It is well known that harmonic analysis plays an important role in partial differential equations
In order to discuss the fractional Carleson measures on the Siegel upper half space, we introduce the p-dimensional Hausdorff capacity and Choquet integral on the Heisenberg group in the following
With Hausdorff capacity on the Heisenberg group discussed above, we introduce the tent spaces on the Siegel upper half space, an analogy of the Coifman-MeyerStein tent space on Rn cf. 4, 6

Summary

Introduction

It is well known that harmonic analysis plays an important role in partial differential equations. The tent spaces on the Siegel upper half space in terms of Choquet integrals with respect to the Hausdorff capacity on the Heisenberg group are introduced. The fractional Carleson measures and the tent spaces on the Siegel upper half space will be used for Q spaces and the Hardy-Hausdorff spaces on the Heisenberg group which will be discussed in another paper by us. The dual of S Hn is S Hn , the space of tempered distributions on Hn

Hausdorff Capacity on Heisenberg Group

Tent Spaces with Hausdorff Capacity