Abstract
In this article we study the problem of extending Fourier Multipliers on L p(T) to those on L p(R) by taking convolution with a kernel, called a summability kernel. We characterize the space of such kernels Λ for the cases p = 1 and p = 2. For other values of p we give a necessary condition for a function Λ to be a summability kernel. For the case p = 1, we present properties of measures which are transferred from M(T) to M(R) by summability kernels. Furthermore it is shown that every l p sequence can be extended to some L q(R) multipliers for certain values of p and q.
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Communicated by Tom Körner.
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Mohanty, P., Madan, S. Summability Kernels for L p Multipliers. J. Fourier Anal. Appl. 9, 127–140 (2003). https://doi.org/10.1007/s00041-003-0007-z
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DOI: https://doi.org/10.1007/s00041-003-0007-z