Multipliers for Hardy spaces on locally compact Vilenkin groups

Journal of the Australian Mathematical Society

C. W. Onneweer¹ 

[1] T. S. Quek

关键词: primary 43 A 22;    secondary 43 A 15;    43 A 70;   

DOI  :  10.1017/S1446788700034042

学科分类：数学（综合）

来源: Cambridge University Press

【 摘 要 】

In a recent paper In a recent paper the authors proved a multiplier theorem for Hardy spaces Hp (G), 0 < p ≤ 1, defined on a locally compact Vilenkin group G. The assumptions on the multiplier were expressed in terms of the “norms” of certain Herz spaces K (1/p − 1/?r, r, p) with r restricted to 1 ≤ r < ∞ and p < r. In the present paper we show how this restriction on r may be weakened to p ≤ r ∞. Furthermore, we present two modifications of our main theorem and compare these with certain results for multipliers on LP (Rn)-spaces, 1 < p < ∞, due to Seeger and to Cowling, Fendler and Foumier. We also discuss the sharpness of some of our results.

【 授权许可】

Unknown