A multiplier theorem for $H^{1}(\textbf {R}^{n})$
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- by Daniel M. Oberlin PDF
- Proc. Amer. Math. Soc. 73 (1979), 83-87 Request permission
Abstract:
We prove the following theorem. Theorem. Let m be a nonnegative measurable function on $[0,\infty )$. For $n \geqslant 2$, the two conditions below are equivalent: (a) $\smallint {\;_{{R^n}}}|\hat f(x)|m(|x|)\;dx < \infty$ for each $f \in {H^1}({R^n})$, (b) $\sup \{ {2^{(n - 1)k}}\smallint _{{2^k}}^{{2^{k + 1}}}m(r)\;dr: - \infty < k < \infty \} < \infty$.References
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Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 73 (1979), 83-87
- MSC: Primary 42B15
- DOI: https://doi.org/10.1090/S0002-9939-1979-0512063-2
- MathSciNet review: 512063