On the norm continuity of the hk-fourier transform

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doi:10.3934/era.2018.25.005

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2018, Volume 25: 36-47. Doi: 10.3934/era.2018.25.005

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On the norm continuity of the hk-fourier transform

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1.
Departamento de Matemáticas, Universidad Autónoma Metropolitana - Iztapalapa, Av. San Rafael Atlixco 186, CDMX, 09340, Mexico
2.
Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Av. San Claudio y 18 Sur S/N, Puebla, 72570, Mexico

Received: February 12, 2018

Published: March 2018

This work is partially supported by CONACyT-SNI and VIEP-BUAP (Puebla, Mexico)

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In this work we study the Cosine Transform operator and the Sine Transform operator in the setting of Henstock-Kurzweil integration theory. We show that these related transformation operators have a very different behavior in the context of Henstock-Kurzweil functions. In fact, while one of them is a bounded operator, the other one is not. This is a generalization of a result of E. Liflyand in the setting of Lebesgue integration.

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Mathematics Subject Classification: Primary: 26A39, 43A32; Secondary: 26A42, 26A45.

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