Convolution operators on Hardy spaces

ArticleOriginal scientific text

Title

Authors ¹

Department of Mathematics, National Central University, Chung-li, Taiwan 32054, Republic of China

We give sufficient conditions on the kernel K for the convolution operator Tf = K ∗ f to be bounded on Hardy spaces

H^{p} (G)

, where G is a homogeneous group.

atomic decomposition, Hardy spaces, homogeneous groups

[CW1] R. R. Coifman and G. Weiss, Analyse Harmonique Non-Commutative sur Certains Espaces Homogènes, Lecture Notes in Math. 242, Springer, Berlin, 1971.
[CW2] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), 569-645.
[FS] G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups, Math. Notes 28, Princeton Univ. Press, Princeton, N.J., 1982.
[HJTW] Y. Han, B. Jawerth, M. Taibleson, and G. Weiss, Littlewood-Paley theory and ϵ-families of operators, Colloq. Math. 60//61 (1990), 321-359.
[L] C.-C. Lin, $L^{p}$ multipliers and their $H^{1}$ - $L^{1}$ estimates on the Heisenberg group, Rev. Mat. Iberoamericana 11 (1995), 269-308.
[S] E. M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1970.
[TW] M. H. Taibleson and G. Weiss, The molecular characterization of certain Hardy spaces, Astérisque 77 (1980), 67-149.