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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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

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

First available in Project Euclid: 14 March 2011

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

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


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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