Regularity of the Hardy Littlewood Function

Regularity of the Hardy Littlewood Function

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Kevin Hughes
Fine Hall 314

$Lp$ boundedness of the Hardy-Littlewood function is a classic result in harmonic analysis. But not much is understood about the regularity of it. For instance, if your function $f$ is in the Sobolev W1,1 space, is its maximal function in$L1$? The answer to this question is unknown, but I will discuss our partial understanding.