ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

-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.

[img] PDF
MON_FUR_MAT_184-3_459_2017.pdf - Published Version
Restricted to Registered users only

Download (570kB) | Request a copy
Official URL: http://doi.org/10.1007/s00605-017-1081-7


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
Date Deposited: 30 Oct 2017 03:41
Last Modified: 30 Oct 2017 03:41
URI: http://eprints.iisc.ac.in/id/eprint/58088

Actions (login required)

View Item View Item