Mathematics Faculty Scholarship

Document Type

Article

Publication Date

7-2011

Publication Title

Journal of Mathematical Analysis and Applications

Keywords

Weight Functions, Fourier Transform

Abstract

We discuss conditions on weight functions, necessary or sufficient, so that the Fourier transform is bounded from one weighted Lebesgue space to another. The sufficient condition and the primary necessary condition presented are similar, one being phrased is terms of arbitrary measurable sets and the other in terms of cubes. We believe that the symmetry amongst the two conditions helps frame how a single condition, necessary and sufficient, might appear.

First Page

439

Last Page

443

Volume

379

Issue

1

Original Citation

Berndt, R. "Symmetric Conditions For A Weighted Fourier Transform Inequality." Journal Of Mathematical Analysis And Applications 379.1 (2011): 439-443.

DOI

10.1016/j.jmaa.2011.01.042

Version

Post-Print

Peer Reviewed

1

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