Abstract
In this note, we consider the multipliers on weighted H1 spaces over totally disconnected locally compact abelian groups with a suitable sequence of open compact subgroups (Vilenkin groups). We first show an (H1, L1) multiplier result from which Onneweer′s theorem follows. We also give an (H1, H1) multiplier result under a condition of Baernstein‐Sawyer type.
Highlights
I) In this note, we show a weighted
We are able to show that a Baernsteln-Sawyer type condition [2] which is stronger than Onneweer’s, implies a
It is easy to see that for each n
Summary
Onneweer obtained a weighted Lp multiplier theorem [I, Theorem I] over a Vilenkln group which is a generalization of Talbleson’s theorem over a local field. I) In this note, we show a weighted We are able to show that a Baernsteln-Sawyer type condition [2] which is stronger than Onneweer’s, implies a This is a generalization of Theorem 2 [2]. Throughout this note, G will denote a locally compact abelian group with a sequence {Gn}...
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