-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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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
Publication:	MONATSHEFTE FUR MATHEMATIK
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
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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