Abstract
Olsen-type inequalities for the generalized commutator of multilinear fractional integrals
Highlights
The classical fractional integral ∫ f (y)Iα(f )(x) = Rn |x − y|n−α dy (0 < α < n) plays important roles in many fields of mathematics
In this paper, we study certain multilinear operators of fractional integral type defined by
For the operator IαA⃗, we obtain an Olsen-type inequality on the Morrey space
Summary
For the operator IαA⃗ , we obtain an Olsen-type inequality on the Morrey space. The operator TΩA later plays an important role in the study of PDEs. For instance, by using the W 1,p estimate for the elliptic equation of divergence form with partial BMO coefficients and the Lp boundedness for a generalized commutator of Cohen–Gosselin type (see [27, 45]), Wang and Zhang in [41] obtained a simple proof for Wu’s theorem (the reader may see [43] for Wu’s theorem). Mo et al [28] studied the following generalized commutator of the multilinear fractional integral defined by
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