# Some new Hardy spaces $L\xb2{H}_{R}^{q}\left(\mathbb{R}{\xb2}_{+}\times \mathbb{R}{\xb2}_{+}\right)$ (0 < q ≤ 1)

Studia Mathematica (1994)

- Volume: 109, Issue: 3, page 217-231
- ISSN: 0039-3223

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topYang, Dachun. "Some new Hardy spaces $L²H^{q}_{R}(ℝ²_{+} × ℝ²_{+})$ (0 < q ≤ 1)." Studia Mathematica 109.3 (1994): 217-231. <http://eudml.org/doc/216071>.

@article{Yang1994,

abstract = {For 0 < q ≤ 1, the author introduces a new Hardy space $L² H^q_ℝ (ℝ²_+ × ℝ²_+)$ on the product domain, and gives its generalized Lusin-area characterization. From this characterization, a φ-transform characterization in M. Frazier and B. Jawerth’s sense is deduced.},

author = {Yang, Dachun},

journal = {Studia Mathematica},

keywords = {central rectangle; Herz space; product domain; central atom; Lusin area function characterization; -transform characterization; Hardy space},

language = {eng},

number = {3},

pages = {217-231},

title = {Some new Hardy spaces $L²H^\{q\}_\{R\}(ℝ²_\{+\} × ℝ²_\{+\})$ (0 < q ≤ 1)},

url = {http://eudml.org/doc/216071},

volume = {109},

year = {1994},

}

TY - JOUR

AU - Yang, Dachun

TI - Some new Hardy spaces $L²H^{q}_{R}(ℝ²_{+} × ℝ²_{+})$ (0 < q ≤ 1)

JO - Studia Mathematica

PY - 1994

VL - 109

IS - 3

SP - 217

EP - 231

AB - For 0 < q ≤ 1, the author introduces a new Hardy space $L² H^q_ℝ (ℝ²_+ × ℝ²_+)$ on the product domain, and gives its generalized Lusin-area characterization. From this characterization, a φ-transform characterization in M. Frazier and B. Jawerth’s sense is deduced.

LA - eng

KW - central rectangle; Herz space; product domain; central atom; Lusin area function characterization; -transform characterization; Hardy space

UR - http://eudml.org/doc/216071

ER -

## References

top- [1] S. A. Chang and R. Fefferman, Some recent developments in Fourier analysis and ${H}^{p}$-theory on product domains, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 1-43. Zbl0557.42007
- [2] S. A. Chang and R. Fefferman, A continuous version of duality of ${H}^{1}$ with BMO on the bidisc, Ann. of Math. 112 (1980), 179-201. Zbl0451.42014
- [3] Y. Z. Chen and K. S. Lau, On some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), 255-278. Zbl0677.30030
- [4] J. Garcí a-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39 (1989), 499-513.
- [5] M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, in: Function Spaces and Applications, M. Cwikel et al. (eds.), Lecture Notes in Math. 1302, Springer, 1989, 223-246.
- [6] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170. Zbl0716.46031
- [7] S. Z. Lu and D. C. Yang, The wavelet characterizations of some new Hardy spaces associated with the Herz spaces, J. Beijing Normal Univ. (Natur. Sci.) 29 (1993), 10-19 (in Chinese). Zbl0782.42019
- [8] 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

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