Let (X,d,μ) be a space of homogeneous type and L be a nonnegative self-adjoint operator on L2(X) whose heat kernels satisfy Gaussian upper bounds. In this article, we introduce the weighted variable Besov space associated with the operator L and demonstrate that Peetre maximal functions can be used to characterize this space. Furthermore, we provide a detailed study of its atomic decompositions.

In this paper, we introduce and study the weighted variable Hardy space ondomains. We prove the atomic decompositions of this space, and as application, wefigure out its dual space.

This paper studies aquifer’s hydrodynamic behavior by combining a flow-simulation model with transmissivity optimization (cokriging) in order to provide an optimal management scheme for the groundwater aquifer. The use of a cokriging approach improves the transmissivity data which are insufficient for the database of the groundwater flow simulation model. The obtained results are then used to model the groundwater flow of the Tebessa-Morsott shallow aquifer, located in NE Algeria, under a steady and transient regime. The results of the model calibration for the steady-state (year 2010) show that the recharge by rainfall and leakage rate are similar compared to those calculated by the analytical approach, (84,354 m3/day for the recharge and 36,986 m3/day for pumped water flow rate). The results of the transient regime show the alluvial aquifer affected by large drawdowns reaching 40 m over 20 years (year 2030 scenario) due to increase in water exploitation from pumping wells to answer water needs of the Tebessa region.