It is proved that, for the nondivergence elliptic equations ∑in, j=1 aijuxixj = f,if f belongs to the generalized Morrey spaces Lp,ψ(ω), then uxixj ∈ Lp,ψ(ω), where u is the W2,p-solution of the equations. In order to obtain this, the author first establish the weighted boundedness for the commutators of some singular integral operators on Lp,ψ (ω).

Interior estimates in morrey spaces for solutions of elliptic equations and weighted boundedness for commutators of singular integral operators

In this paper, we establish the weighted sharp maximal function inequalities for the multilinear operator associated with the singular integral operator satisfying a variant of Hormander’s condition. As an application, we obtain the boundedness of the operator on weighted Lebesgue spaces. MSC:42B20, 42B25.

/pdf/weighted-sharp-maximal-function-inequalities-and-boundedness-b19ap6uusp.pdf

Weighted sharp maximal function inequalities and boundedness of multilinear singular integral operator satisfying a variant of Hörmander’s condition

In this paper, we establish the weighted sharp maximal function inequalities for the multilinear operator associated to the singular integral operator satisfying a variant of Hormander’s condition. As an application, we obtain the boundedness of the operator on weighted Lebesgue and Morrey spaces.

https://jyotiacademicpress.net/weighted_boundedness_of_multilinear.pdf

Weighted boundedness of multilinear operator associated to singular integral operator satisfying a variant of hörmander's condition

Estimation of Commutators ofSingular Integral OperatorsSatisfying a Variant of Hormander'sCondition

In this paper, we prove the M k -type sharp maximal function estimates for the commutators related to some singular integral operators satisfying a variant of Hormander's condition. As an application, we obtain the weighted boundedness of the commutators on Lebesgue and Morrey spaces.

/pdf/m-2-type-sharp-estimates-and-weighted-boundedness-for-2a3s8k0dea.pdf

M 2 -Type Sharp Estimates and Weighted Boundedness for Commutators Related to Singular Integral Operators Satisfying a Variant of Hörmander's Condition

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M 2 -Type Sharp Estimates and Weighted Boundedness for Commutators Related to Singular Integral Operators Satisfying a Variant of Hörmander's Condition