Recently, continuous functionals for unbounded order (norm, weak and weak*) in Banach lattices were studied. In this paper, we study the operators with respect to convergences. We first investigate approximation property of convergence. Then show some characterizations continuity uo, un, uaw uaw*-convergence. Based on these results, discuss order-weakly compact lattices.

We suggest an elementary harmonic analysis approach to canceling and weakly differential operators, which allows us extend these notions the anisotropic setting replace operators with Fourier multiplies mild smoothness regularity. In this more general of multipliers, we prove inequality $$\|f\|_{L_\infty} \lesssim \|Af\|_{L_1}$$ if $$A$$ is a operator order $$d$$ $$\|f\|_{L_2} $$d/2$$ , provide...

It is the objective of this paper to introduce a new class of generalizations of continuous functions via λ-open sets called weakly λcontinuous functions. Moreover, we study some of its fundamental properties. It turns out that weak λ-continuity is weaker than λ-continuity [1]. AMS Mathematics Subject Classification (2000): 54C10, 54D10