Some new inequalities for the Fourier transform for functions in generalized Lorentz spaces

Aigerim Nurzhanovna Kopezhanova

Some new inequalities for the Fourier transform for functions in generalized Lorentz spaces

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Authors

Aigerim Nurzhanovna Kopezhanova

Keywords:

Fourier transform, Hausdorff–Young's inequality, generalized Lorentz spaces, weight function, generalized monotone function

Abstract

The classical Hausdorff–Young and Hardy–Littlewood–Stein inequalities, relating functions on ℝ and their Fourier transforms, are extended and complemented in various ways. In particular, a variant of the Hardy–Littlewood–Stein inequality covering the case \( p > 2 \) is proved and two-sided estimates are derived.

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Published

2017-03-30

How to Cite

Kopezhanova, A. N. (2017). Some new inequalities for the Fourier transform for functions in generalized Lorentz spaces. Eurasian Mathematical Journal, 8(1), 58–66. Retrieved from https://emj.enu.kz/index.php/main/article/view/655