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1995 | 116 | 2 | 103-131
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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 $HK_q^{α,p}(ℝ^n)$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
116
Numer
2
Strony
103-131
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-12-13
poprawiono
1995-03-22
Twórcy
autor
  • Department of Mathematics, Beijing Normal University, Beijing 100875, The People's Republic of China
autor
  • Department of Mathematics, Beijing Normal University, Beijing 100875, The People's Republic of China
Bibliografia
  • [1] A. Baernstein II and E. T. Sawyer, Embedding and multiplier theorems for $H^p(ℝ^n)$, Mem. Amer. Math. Soc. 318 (1985).
  • [2] Y. Z. Chen and K. S. Lau, On some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), 255-278.
  • [3] C. Fefferman and E. M. Stein, $H^p$ spaces of several variables, Acta Math. 129 (1972), 137-193.
  • [4] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Univ. Math. J. 34 (1985), 777-799.
  • [5] M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, in: Lecture Notes in Math. 1302, Springer, 1988, 223-246.
  • [6] M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.
  • [7] J. García-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39 (1989), 499-513.
  • [8] S. Z. Lu and F. Soria, On the Herz spaces with power weights, in: Fourier Analysis and Partial Differential Equations, J. Garcí a-Cuerva, E. Hernández, F. Soria and J. L. Torrea (eds.), Stud. Adv. Math., CRC Press, Boca Raton, 1995, 227-236.
  • [9] 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.
  • [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.
  • [11] M. H. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Astérisque 77 (1980), 67-149.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv116i2p103bwm
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