On One Weighted Inequalities for Convolution Type Operator

Authors : R A B

Pages : 199-210

View : 21 | Download : 10

Publication Date : 2013-03-01

Article Type : Other Papers

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¨ormanders condition, Boundedness