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arXiv · 1306.4494

$L^p$-integrability, dimensions of supports of fourier transforms and applications

K. S. Senthil Raani
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Abstract

It is proved that there does not exist any non zero function in $L^p(\R^n)$ with $1\leq p\leq 2n/α$ if its Fourier transform is supported by a set of finite packing $α$-measure where $0<α 2n/α$. The result is applied to prove $L^p$ Wiener-Tauberian theorems for $\R^n$ and M(2).

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K. S. Senthil Raani. 2014-05-14. $L^p$-integrability, dimensions of supports of fourier transforms and applications. https://doi.org/10.1007/s00041-014-9334-5

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