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

• Autorzy: Dachun Yang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 42B25: Maximal functions, Littlewood-Paley theory
• 42C15: General harmonic expansions, frames

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1994
• Tom: 109
• Numer: 3
• Strony: 217-231

Daty

wydano

1994

otrzymano

1992-04-23

poprawiono

1993-09-09

Twórcy

autor

Dachun Yang

• Department of Mathematics, Beijing Normal University, 100875 Beijing, P.R. China

Bibliografia

• [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.
• [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.
• [3] Y. Z. Chen and K. S. Lau, On some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), 255-278.
• [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.
• [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).
• [8] S. Z. Lu and D. C. Yang, The Littlewood-Paley function and φ-transform characterizations of a new Hardy space $HK_2$ associated with the Herz space, Studia Math. 101 (1992), 285-298.