Continuity of Bilinear Fractional Maximal Commutators with Lipschitz Symbols in Sobolev Spaces

Abstract

We establish the continuity of bilinear fractional maximal commutator with Lipschitz symbols in Sobolev spaces, both in the global and local cases. The main ingredients of proving the main results are some new pointwise estimates for the weak derivatives of the above commutators. The continuity result in global case answers a question originally motivated by Wang and Liu in [Math. Inequal. Appl., 2022, 25(2): 573–600].

Keywords

Bilinear fractional maximal commutator / Lipschitz symbol / Sobolev space / continuity / 42B25 / 46E35

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Peking University