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-Fourier asymptotics, Hardy-type inequality and fractal measures

Raani, K S Senthil (2017) -Fourier asymptotics, Hardy-type inequality and fractal measures. In: MONATSHEFTE FUR MATHEMATIK, 184 (3). pp. 459-487.

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Official URL: http://doi.org/10.1007/s00605-017-1081-7

Abstract

Suppose is an -dimensional fractal measure for some . Inspired by the results proved by Strichartz (J Funct Anal 89:154-187, 1990), we discuss the -asymptotics of the Fourier transform of by estimating bounds of lim inf(L ->infinity) 1/L-k integral vertical bar xi vertical bar <= L vertical bar(integral d mu) over cap(xi)vertical bar(p)d xi for and . In a different direction, we prove a Hardy type inequality, that is, integral vertical bar f(x)vertical bar(p)/(mu(E-x))(2-p)d mu(x) <= C lim inf(L ->infinity) 1/Ln-alpha integral B-L(0)(integral d mu) over cap(xi)vertical bar(p)d xi where and for generalizing the one dimensional results by Hudson and Leckband (J Funct Anal 108:133-160, 1992).

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the SPRINGER WIEN, SACHSENPLATZ 4-6, PO BOX 89, A-1201 WIEN, AUSTRIA
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Depositing User: Id for Latest eprints
Date Deposited: 30 Oct 2017 03:41
Last Modified: 30 Oct 2017 03:41
URI: http://eprints.iisc.ac.in/id/eprint/58088

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