The L(log L)^ε endpoint estimate for maximal singular integral operators

2015/03/13 by Hytönen, Tuomas, Pérez, Carlos
#42B20 #42B25 #46E30 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1503.04008

Abstract

We prove in this paper the following estimate for the maximal operator T^* associated to the singular integral operator T: ‖T^*f‖_L^1,∞(w) \lesssim \frac1ε ∫_ℝⁿ |f(x)| M_{L(log L)^ε} (w)(x)dx, for w≥ 0, 0

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