TWO WEIGHT CHARACTERIZATIONS FOR THE MULTILINEAR LOCAL MAXIMAL OPERATORS

Let 0<β<1 andΩbe a proper open and non-empty subset of R^(n).In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_(β)((f))(x)=sup_(Q(∈)xQ∈Fβ)Π_(i=1)^m1/|Q|∫_(Q)|f_(i)(y_(i))|dy_(i),where F_(β)={Q(x,l):x∈Ω,l<βd(x,Ω^(c))},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator M_(β)are obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved.

Boundedness of Multilinear Oscillatory Singular Integral on Weighted Weak Hardy Spaces

In this paper, by using the atomic decomposition of the weighted weak Hardy space WH;（R;）, the authors discuss a class of multilinear oscillatory singular integrals and obtain their boundedness from the weighted weak Hardy space WH;（R;） to the weighted weak Lebesgue space WL;（R;） for ω∈A;（R;）.

Recovering rare earth elements via immobilized red algae from ammonium-rich wastewater

Biotreatment of acidic rare earth mining wastewater via acidophilic living organisms is a promising approach owing to their high tolerance to high concentrations of rare earth elements(REEs);however,simultaneous removal of both REEs and ammonium is generally hindered since most acidophilic organisms are positively charged.Accordingly,immobilization of acidophilic Galdieria sulphuraria(G.sulphuraria)by calcium alginate to improve its affinity to positively charged REEs has been used for simultaneous bioremoval of REEs and ammonium.The results indicate that 97.19%,96.19%,and 98.87%of La,Y,and Sm,respectively,are removed by G.sulphuraria beads(GS-BDs).The adsorption of REEs by calcium alginate beads(BDs)and GS-BDs is well fitted by both pseudo first-order(PFO)and pseudo second-order(PSO)kinetic models,implying that adsorption of REEs involves both physical adsorption caused by affinity of functional groups such as-COO-and -OH and chemical adsorption based on ion exchange of Ca^(2+) with REEs.Notably,GS-BDs exhibit high tolerance to La,Y,and Sm with maximum removal efficiencies of 97.9%,96.6%,and 99.1%,respectively.Furthermore,the ammonium removal efficiency of GS-BDs is higher than that of free G.sulphuraria cells at an initial ammonium concentration of 100 mg L^(-1),while the efficiency decreases when initial concentration of ammonium is higher than 150 mg L^(-1).Last,small size of GS-BDs favors ammonium removal because of their lower mass transfer resistance.This study achieves simultaneous removal of REEs and ammonium from acidic mining drainage,providing a potential strategy for biotreatment of REE tailing wastewater.