Hokkaido Mathematical Journal

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

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

Hokkaido Mathematical Journal, 40 (2011) pp.1-32

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Abstract

In this paper, we study the Lp boundedness of a class of maximal operators T{Ωj}(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.

MSC(Primary)42B20
MSC(Secondary)42B15, 42B25
Uncontrolled Keywordsmaximal operator, rough kernel, L log L spaces, block spaces, singular integral, Lp boundedness, product spaces