On $H^p(\mathbf {R}^n)$-multipliers of mixed-norm type
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- by C. W. Onneweer and T. S. Quek PDF
- Proc. Amer. Math. Soc. 121 (1994), 543-552 Request permission
Abstract:
For a function m in ${L^\infty }({{\mathbf {R}}^n})$, an appropriately chosen function $\eta$ in ${C^\infty }({{\mathbf {R}}^n})$ and $\delta > 0$ we define ${m_\delta }$ by ${m_\delta }(\xi ) = m(\delta \xi )\eta (\xi )$. We show that if $0 < p \leq 1$ and if the sequence $((m_{2^n})\hat \emptyset )$ belongs to a certain mixed-norm space, depending on p, then m is a Fourier multiplier for the corresponding Hardy space ${H^p}({{\mathbf {R}}^n})$. Moreover, we prove the sharpness of our multiplier theorem. Comparable results had been proved earlier for multipliers for Hardy spaces defined on a locally compact Vilenkin group.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 543-552
- MSC: Primary 42B15; Secondary 42B30, 46E99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1204383-1
- MathSciNet review: 1204383