# The local versions of ${H}^{p}\left({\mathbb{R}}^{n}\right)$ spaces at the origin

Studia Mathematica (1995)

- Volume: 116, Issue: 2, page 103-131
- ISSN: 0039-3223

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topLu, Shan, and Yang, Da. "The local versions of $H^p(ℝ^n)$ spaces at the origin." Studia Mathematica 116.2 (1995): 103-131. <http://eudml.org/doc/216223>.

@article{Lu1995,

abstract = {Let 0 < p ≤ 1 < q < ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces $HK̇_q^\{α,p\}(ℝ^n)$ 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 $HK̇_q^\{α,p\}(ℝ^n)$ and discuss the $HK̇_q^\{α,p\}(ℝ^n)$-boundedness of Calderón-Zygmund operators. Similar results can also be obtained for the non-homogeneous Hardy spaces $HK_q^\{α,p\}(ℝ^n)$.},

author = {Lu, Shan, Yang, Da},

journal = {Studia Mathematica},

keywords = {Herz spaces; Hardy spaces; local versions; atomic and molecular decompositions; -transform; Calderón-Zygmund operators},

language = {eng},

number = {2},

pages = {103-131},

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

url = {http://eudml.org/doc/216223},

volume = {116},

year = {1995},

}

TY - JOUR

AU - Lu, Shan

AU - Yang, Da

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

JO - Studia Mathematica

PY - 1995

VL - 116

IS - 2

SP - 103

EP - 131

AB - Let 0 < p ≤ 1 < q < ∞ and α = n(1/p - 1/q). We introduce some new Hardy spaces $HK̇_q^{α,p}(ℝ^n)$ 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 $HK̇_q^{α,p}(ℝ^n)$ and discuss the $HK̇_q^{α,p}(ℝ^n)$-boundedness of Calderón-Zygmund operators. Similar results can also be obtained for the non-homogeneous Hardy spaces $HK_q^{α,p}(ℝ^n)$.

LA - eng

KW - Herz spaces; Hardy spaces; local versions; atomic and molecular decompositions; -transform; Calderón-Zygmund operators

UR - http://eudml.org/doc/216223

ER -

## References

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- [9] S. Z. Lu and D. C. Yang, The Littlewood-Paley function and φ-transform characterizations of a new Hardy space $H{K}_{2}$ associated with the Herz space, Studia Math. 101 (1992), 285-298. Zbl0811.42005
- [10] S. Z. Lu and D. C. Yang, Some new Hardy spaces associated with the Herz spaces and their wavelet characterizations, J. Beijing Normal Univ. (Natural Sci.) 29 (1993), 10-19. Zbl0782.42019
- [11] M. H. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Astérisque 77 (1980), 67-149. Zbl0472.46041
- [12] M. H. Taibleson and G. Weiss, Certain function spaces associated with a.e. convergence of Fourier series, in: Conference in Honor of A. Zygmund, Vol. I, Wadsworth, 1983, 95-113.

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