The local versions of $H^p(ℝ^n)$ spaces at the origin

Shan Zhen Lu; Da Yang

ArticleOriginal scientific text

Title

The local versions of $H^{p} (ℝ^{n})$ spaces at the origin

Authors ¹, ¹

Affiliations

Department of Mathematics, Beijing Normal University, Beijing 100875, The People's Republic of China

Abstract

Let 0 < p ≤ 1 < q < ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces

H K ̇_{q}^{α, p} (ℝ^{n})

which are the local versions of

H^{p} (ℝ^{n})

spaces at the origin. Characterizations of these spaces in terms of atomic and molecular decompositions are established, together with their φ-transform characterizations in M. Frazier and B. Jawerth's sense. We also prove an interpolation theorem for operators on

H K ̇_{q}^{α, p} (ℝ^{n})

and discuss the

H K ̇_{q}^{α, p} (ℝ^{n})

-boundedness of Calderón-Zygmund operators. Similar results can also be obtained for the non-homogeneous Hardy spaces

H K_{q}^{α, p} (ℝ^{n})

.

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Title

The local versions of Hp(ℝn) spaces at the origin

Affiliations

Abstract

Bibliography

The local versions of $H^{p} (ℝ^{n})$ spaces at the origin