The A-Integral and Restricted Riesz Transform

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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