On One Weighted Inequalities for Convolution Type Operator

Abstract

In this paper we prove the boundedness of certain convolution operatorin a weighted Lebesgue space with kernel satisfying the generalizedH¨ ormander’s condition. The sufficient conditions for the pair of generalweights ensuring the validity of two-weight inequalities of a strong typeand of a weak type for convolution operator with kernel satisfying thegeneralized H¨ormander’s condition are found.

Keywords

• Weighted Lebesgue space, Singular integral, Kernel, Generalized H¨ormander’s condition, Boundedness.

On One Weighted Inequalities for Convolution Type Operator

Abstract

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Keywords

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References

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