A Characterization of Approximation of Hardy Operators in VLS

Abstract

Variable exponent spaces and Hardy operator space have played an important role in recent harmonic analysis because they have an interesting norm including both local and global properties. The variable exponent Lebesgue spaces are of interest for their applications to modeling problems in physics, and to the study of variational integrals and partial differential equations with non-standard growth conditions. This studies also has been stimulated by problems of elasticity, fluid dynamics, calculus of variations, and differential equations with non-standard growth conditions. In this study, we will discuss a characterization of approximation of Hardy operators in variable Lebesgue spaces.

New Exact Solutions for the Klein-Gordon Equation

“…In this section, the application of the improved Bernoulli sub-equation function method to the Klein-Gordon Equation is discussed. Using the wave transformation on equation (1) ∅( , ) = ( ), = −…”

“…Solving the system of the algebraic equations gives the values of the relevant parameter. Substituting the obtained values of the parameters into equation 13, gives the solutions to equation (1).…”

“…Nonlinear evolution equations (NLEEs) are widely used because it finds application in many nonlinear disciplines such as plasma physics, optical fibers, fluid mechanics, fluid dynamics [1][2][3][4] and so on. One of the best known of these equations is Klein-Gordon equation (KGE).…”

Compactness of Fractional Maximal Operator in Weighted and Variable Exponent Spaces

“…In this paper, we will prove compactness of weighted the fractional maximal operator in weighted and variable exponent spaces. Operator theory were worked by very mathematicien (Akin L. 2018;Akin and Zeren, 2017). Recently a considerable number of research has been carried out on the study of generalized Orlicz-Lebesgue spaces L p(x) , Orlicz-Sobolev spaces W 1,p(x) , and the boundedness of different integral operators.…”

A Characterization of Some Class Nonlinear Eigenvalue Problem in VELS

“…A maximally weak condition is assumed on the exponent function. The last time, such a study was carry out in [1,2,3,4,5,6,7,8,9,13,14]. For a study the Dirichlet problem of some class nonlinear eigenvalue problem with nonstandard growth condition the obtained results is applied.…”