A boundedness result for Marcinkiewicz integral operator

Author:

Hawawsheh Laith1,Abudayah Mohammad1

Affiliation:

1. School of Basic Sciences and Humanities, German Jordanian University , Amman , Jordan

Abstract

Abstract We extend a boundedness result for Marcinkiewicz integral operator. We find a new space of radial functions for which this class of singular integral operators remains L p {L}^{p} -bounded when its kernel satisfies only the sole integrability condition.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Reference14 articles.

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2. A. Al-Salman and H. Al-Qassem, On the Lp boundedness of rough parametric Marcinkiewicz functions, J. Inequal. Pure Appl. Math. 8 (2007), no. 4, 108–125.

3. A. Al-Salman, H. Al-Qassem, L. Cheng, and Y. Pan, Lp bounds for the function of Marcinkiewicz, Math. Res. Lett. 9 (2002), no. 5, 697–700.

4. Y. Ding, S. Lu, and K. Yabuta, A problem on rough parametric Marcinkiewicz functions, J. Aust. Math. Soc. 72 (2002), no. 1, 13–21.

5. L. Hawawsheh, A. Al-Salman, and S. Momani, A note on rough parametric Marcinkiewicz functions, Anal. Theory Appl. 35 (2019), no. 1, 40–47.

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