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arXiv · 2004.09687

Regularity property of some operators on Lipschitz spaces and homogeneous Lipschitz spaces related to biharmonic operator

Chao Zhang
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Abstract

In this paper, we consider the characterizations of the Lipschitz spaces and homogeneous Lipschitz spaces associated to the biharmonic operator $\Delta^2.$ With this characterizations, we prove the boundedness of the Bessel potentials, fractional integrals, fractional powers, Riesz transforms and multipliers of Laplace transforms type associated to $\Delta^2$ on Lipschitz spaces and homogeneous Lipschitz spaces. The proofs of these results need the language of semigroups in an essential way.

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Chao Zhang. 2020-04-21. Regularity property of some operators on Lipschitz spaces and homogeneous Lipschitz spaces related to biharmonic operator. https://arxiv.org/abs/2004.09687

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