Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework

Bartosz Langowski; Adam Nowak

doi:10.1016/j.jmaa.2021.125061

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arXiv · 2005.12223

Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework

Bartosz Langowski·Adam Nowak

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Abstract

We prove sharp power-weighted $L^p$, weak type and restricted weak type inequalities for the heat semigroup maximal operator and Riesz transforms associated with the Bessel operator $B_{\nu}$ in the exotic range of the parameter $-\infty < \nu < 1$. Moreover, in the same framework, we characterize basic mapping properties for other fundamental harmonic analysis operators, including the heat semigroup based vertical $g$-function and fractional integrals (Riesz potential operators).

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BibTeX RIS

Bartosz Langowski, Adam Nowak. 2020-05-25. Mapping properties of fundamental harmonic analysis operators in the exotic Bessel framework. https://doi.org/10.1016/j.jmaa.2021.125061

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