Maximal operators related to block spaces

H. M. Al-Qassem

doi:10.2996/kmj/1134397763

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Home > Journals > Kodai Math. J. > Volume 28 > Issue 3 > Article

October 2005 Maximal operators related to block spaces

H. M. Al-Qassem

Kodai Math. J. 28(3): 494-510 (October 2005). DOI: 10.2996/kmj/1134397763

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Abstract

In this paper, we prove appropriate L^p bounds for a class of maximal operators $\mathscr{S}_\Omega$ related to singular integrals with kernels which belong to block spaces and are supported by subvarieties. Also, we show that our condition on the kernel is optimal for the L² boundedness of $\mathscr{S}_\Omega$. Our results improve substantially the main result obtained by L. K. Chen and H. Lin in [CL].