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arXiv · 1711.01484

Regularity of maximal functions on Hardy-Sobolev spaces

Carlos Pérez·Tiago Picon·Olli Saari·Mateus Sousa
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Abstract

We prove that maximal operators of convolution type associated to smooth kernels are bounded in the homogeneous Hardy-Sobolev spaces $\dot{H}^{1,p}(\mathbb{R}^d)$ when $1/p < 1+1/d$. This range of exponents is sharp. As a by-product of the proof, we obtain similar results for the local Hardy-Sobolev spaces $\dot{h}^{1,p}(\mathbb{R}^d)$ in the same range of exponents.

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Carlos Pérez, Tiago Picon, Olli Saari, Mateus Sousa. 2017-11-04. Regularity of maximal functions on Hardy-Sobolev spaces. https://doi.org/10.1112/blms.12195

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