Abstract The concentration-compactness principle of Lions type in Euclidean space relies on the Pólya-Szegö inequality, which is not available non-Euclidean settings. first proof setting, such as Heisenberg group, was given by Li et al. using a symmetrization-free nonsmooth truncation argument. In this article, we study second-order Adams’ inequality Lorentz-Sobolev <m:math xmlns:m="http://www....

We establish a Maz’ya type capacitary inequality which resolves special case of conjecture by David R. Adams. As consequence, we obtain several equivalent norms for Choquet integrals associated to Bessel or Riesz capacities. This enables us bounds the Hardy–Littlewood maximal function in sublinear setting.

holds with some positive constant N . We refer to this inequality as “quasiadditivity”. Quasiadditivity for decompositions into spherical shells has been considered by Landkof [9, Lemma 5.5 in p.304] and Adams [1, Theorem 7.5]. In the case of Green energy (for the definition see Section 5), quasiadditivity for the Whitney decomposition (cf. [14, p.16]) of a half space is discussed in Essén [5]....

The aim of this paper is to establish higher order Poincaré-Sobolev, Hardy-Sobolev-Maz'ya, Adams and Hardy-Adams inequalities on Siegel domains complex hyperbolic spaces using the method Helgason-Fourier analysis spaces. Firstly, we give a factorization theorem for operators space which closely related Geller's operator, as well CR invariant differential Heisenberg group sphere. (See Theorem 1....

The theory of fuzzy measures and fuzzy integrals was introduced by Sugeno [24] as a tool for modeling nondeterministic problems. Sugeno’s integral is analogous to Lebesgue integral which has been studied by many authors, including Pap [18], Ralescu and Adams [19] and, Wang and Klir [25], among others. RománFlores et al [9, 20–23], started the studies of inequalities for Sugeno integral, and the...

A numerical method for the resolution of a system of ordinary differential equations coupled with a mixed constrained minimization problem is presented. This coupling induces discontinuities of some time-dependent variables when inequality constraints are activated or deactivated. The ordinary differential equations are discretized in time and combined with the first order optimality conditions...