Boundedness of p-Adic Integral Operators on Function Spaces

Abstract

In this thesis, we focus on the boundedness of p-adic integral operators on p-adic function spaces. We prove the boundedness of p-adic generalized Hausdorff operator on weighted p-adic Herz and Morrey-type spaces. We also take into account the boundedness of commutator of same operator by considering symbol function either from central BMO spaces or Lipschitz spaces defined on the local field Qn p . Also, we introduce p-adic analog of fractional Hausdorff operator and prove weak and strong type estimates for it and related commutators. We compute sharp weak bounds for Hardy operator and its adjoint operator. Furthermore, we establish the boundedness of weighted multilinear p-adic Hardy operators on product of Herz-type spaces. Most of these results (in the form of chapter in this thesis) has been published and remaining is under review in renowned journals of mathematical science.