Local Boundedness Of Integral Operators In Weighted Amalgam Spaces

In this paper,local boundedness of integral operators in weighted Amalgam spaces are studied.First,some properties of local weights are proved.Secodly,Local Vitali covering lemma is used to prove that good inequality is valid in the local weight,and the local maximum operator is used to control the singular integral operator in the local weight sense,and then the locally weighted boundedness of singular integral operator is obtained.Finally,the locally weighted Amalgam spaces is defined and the locally weighted boundedness of integral operator on the locally weighted Amalgam spaces is obtained by using some properties of local weight,locally weighted boundedness of singular integral operator and local Whitney covering lemma.