The A-Integral and Restricted Riesz Transform

Year 2020, Volume: 3 Issue: 3, 104 - 112, 14.09.2020

Rashid Aliev , Khanim Nebiyeva

https://doi.org/10.33205/cma.728156

Abstract

It is known that the restricted Riesz transform of a Lebesgue integrable function is not Lebesgue integrable. In this paper we prove that the restricted Riesz transform of a Lebesgue integrable function is A-integrable and the analogue of Riesz's equality holds.

ABSTRACT.It is known that the restricted Riesz transform of a Lebesgue integrable function is not Lebesgue inte-grable. In this paper, we prove that the restricted Riesz transform of a Lebesgue integrable function isA-integrableand the analogue of Riesz’s equality holds

Keywords

Riesz transform, A-integral, Riesz's inequality, covering theorem

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