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Licensed Unlicensed Requires Authentication Published by De Gruyter September 27, 2017

Fourier transforms of powers of well-behaved 2D real analytic functions

  • Michael Greenblatt ORCID logo EMAIL logo
From the journal Forum Mathematicum


This paper is a companion paper to [6], where sharp estimates are proven for Fourier transforms of compactly supported functions built out of two-dimensional real-analytic functions. The theorems of [6] are stated in a rather general form. In this paper, we expand on the results of [6] and show that there is a class of “well-behaved” functions that contains a number of relevant examples for which such estimates can be explicitly described in terms of the Newton polygon of the function. We will further see that for a subclass of these functions, one can prove noticeably more precise estimates, again in an explicitly describable way.

MSC 2010: 42B20

Communicated by Christopher D. Sogge


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Received: 2016-12-18
Revised: 2017-4-9
Published Online: 2017-9-27
Published in Print: 2018-5-1

© 2018 Walter de Gruyter GmbH, Berlin/Boston

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