Estimates of gradient of $\mathcal{L}$ -harmonic functions for nonlocal operators with order $α>1$

preprint2022arXivOpen access

We obtain Grönwall type estimates for the gradient of the harmonic functions for a Lévy operator with order strictly larger than 1 and minimal assumptions of its Lévy measure.

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Estimates of gradient of $\mathcal{L}$ -harmonic functions for nonlocal operators with order $α>1$

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Estimates of gradient of L\mathcal{L}L-harmonic functions for nonlocal operators with order α>1α>1α>1

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Estimates of gradient of $\mathcal{L}$ -harmonic functions for nonlocal operators with order $α>1$