The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space

Shanzhen Lu; Dachun Yang

ArticleOriginal scientific text

Title

The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space

Authors ¹, ²

Affiliations

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

Abstract

We give a Littlewood-Paley function characterization of a new Hardy space HK₂ and its φ-transform characterizations in M. Frazier & B. Jawerth's sense.

Y. Z. Chen and K. S. Lau, On some new classes of Hardy spaces, J. Funct. Anal. 84 (1989), 255-278.
C. Fefferman and E. M. Stein, $H^{p}$ spaces of several variables, Acta Math. 129 (1972), 137-193.
M. Frazier and B. Jawerth, The φ-transform and applications to distribution spaces, in: Function Spaces and Applications, Lecture Notes in Math. 1302, Springer, 1988, 223-246.
M. Frazier and B. Jawerth, A discrete transform and decompositions of distribution spaces, J. Funct. Anal. 93 (1990), 34-170.
J. García-Cuerva, Hardy spaces and Beurling algebras, J. London Math. Soc. (2) 39 (1989), 499-513.
C. Herz, Lipschitz spaces and Bernstein's theorem on absolutely convergent Fourier transform, J. Math. Mech. 18 (1968), 283-324.
D. S. Kurtz, Littlewood-Paley operators on BMO, Proc. Amer. Math. Soc. 99 (1987), 657-666.
S. Lu and D. Yang, Some new Hardy spaces associated with the Herz spaces, to appear.
A. Torchinsky, Real-variable Methods in Harmonic Analysis, Academic Press, New York 1986.
D. Yang, The boundedness of generalized Littlewood-Paley functions, Chinese Ann. Math. Ser. A 12 (1991), 736-744.

Title

The Littlewood-Paley function and φ-trans-form characterizations of a new Hardy space HK₂ associated with the Herz space

Affiliations

Abstract

Bibliography