Hokkaido Mathematical Journal

On the boundedness of a class of rough maximal operators on product spaces

Hussain M. AL-QASSEM, Leslie C. CHENG, and Yibiao PAN

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Abstract

In this paper, we study the Lp boundedness of a class of maximal operators Tj}(γ) and a related class of rough singular integrals on product spaces. We obtain appropriate Lp estimates for such maximal operators and singular integrals. These estimates are used in an extrapolation argument and allow us to obtain some new and improved results for certain maximal integral operators and singular integrals on product spaces under certain sharp conditions on the kernel functions. Also, one of our main results in this paper is a corrigendum of a result obtained by Ding-Lin.

Article information

Source
Hokkaido Math. J., Volume 40, Number 1 (2011), 1-32.

Dates
First available in Project Euclid: 14 March 2011

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1300108396

Digital Object Identifier
doi:10.14492/hokmj/1300108396

Mathematical Reviews number (MathSciNet)
MR2790827

Zentralblatt MATH identifier
1220.42011

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 42B15: Multipliers 42B25: Maximal functions, Littlewood-Paley theory

Keywords
maximal operator rough kernel L log L spaces block spaces singular integral Lp boundedness product spaces

Citation

AL-QASSEM, Hussain M.; CHENG, Leslie C.; PAN, Yibiao. On the boundedness of a class of rough maximal operators on product spaces. Hokkaido Math. J. 40 (2011), no. 1, 1--32. doi:10.14492/hokmj/1300108396. https://projecteuclid.org/euclid.hokmj/1300108396


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