GRADIENT ESTIMATES FOR THE COMMUTATOR WITH FRACTIONAL DIFFERENTIATION FOR SECOND ORDER ELLIPTIC OPERATORS

doi:10.1007/s10473-019-0505-y

Abstract

Abstract: Let L=-div(A∇) be a second order divergence form elliptic operator, where A is an accretive, n×n matrix with bounded measurable complex coefficients on Rⁿ. Let L^α/2 (0 < α < 1) denotes the fractional differential operator associated with L and (-∆)^α/2b ∈ L^n/α(Rⁿ). In this article, we prove that the commutator[b, L^α/2] is bounded from the homogenous Sobolev space L_α² (Rⁿ) to L²(Rⁿ).

Key words: commutator, fractional differentiation, elliptic operators, Sobolev space

CLC Number:

42B20

Wenyu TAO, Yanping CHEN, Jili LI. GRADIENT ESTIMATES FOR THE COMMUTATOR WITH FRACTIONAL DIFFERENTIATION FOR SECOND ORDER ELLIPTIC OPERATORS[J].Acta mathematica scientia,Series B, 2019, 39(5): 1255-1264.

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References

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