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L p estimates of rough maximal functions along surfaces with applications

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Abstract

In this paper, we study the L p mapping properties of certain class of maximal oscillatory singular integral operators. We prove a general theorem for a class of maximal functions along surfaces. As a consequence of such theorem, we establish the L p boundedness of various maximal oscillatory singular integrals provided that their kernels belong to the natural space Llog L(S n−1). Moreover, we highlight some additional results concerning operators with kernels in certain block spaces. The results in this paper substantially improve previously known results.

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Authors and Affiliations

  1. Department of Mathematics, Yarmouk University, Irbid, Jordan

    Ahmad Al-Salman & Abdulla M. Jarrah

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  1. Ahmad Al-Salman
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  2. Abdulla M. Jarrah
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Correspondence to Ahmad Al-Salman.

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Al-Salman, A., Jarrah, A.M. L p estimates of rough maximal functions along surfaces with applications. Acta. Math. Sin.-English Ser. 32, 925–942 (2016). https://doi.org/10.1007/s10114-016-5274-0

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  • DOI: https://doi.org/10.1007/s10114-016-5274-0

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