Applying the convolution to study some properties on the local bounded and local integrable function class

Abstract

In this paper, we are going to use convolution to establish several results concerning the class of integrable and locally bounded functions. In [1], the author has proven the estimation of the subharmonic functions by the family of smooth subharmonic functions. In the present work, the authors extend this technique to a wider function class of integrable and locally bounded functions. Specifically, the authors have used convolution to construct smooth subharmonic functions from the functions of local bound and local integration and studied some properties of these functions. Building on these results, the authors derive a stronger result that omits the local bound of the original function.