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arXiv · 2102.04748

New estimates for the maximal functions and applications

Oscar Domínguez·Sergey Tikhonov
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Abstract

In this paper we study sharp pointwise inequalities for maximal operators. In particular, we strengthen DeVore's inequality for the moduli of smoothness and a logarithmic variant of Bennett--DeVore--Sharpley's inequality for rearrangements. As a consequence, we improve the classical Stein--Zygmund embedding deriving $\dot{B}^{d/p}_\infty L_{p,\infty}(\mathbb{R}^d) \hookrightarrow \text{BMO}(\mathbb{R}^d)$ for $1 < p < \infty$. Moreover, these results are also applied to establish new Fefferman--Stein inequalities, Calder\'on--Scott type inequalities, and extrapolation estimates. Our approach is based on the limiting interpolation techniques.

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Oscar Domínguez, Sergey Tikhonov. 2021-02-09. New estimates for the maximal functions and applications. https://arxiv.org/abs/2102.04748

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