We denote by Lloc(IR) the space of locally integrable functions f : IR 7→ IR. These are the Lebesgue measurable functions which are integrable over every bounded interval. The support of a function φ, denoted by Supp(φ), is the closure of the set {x ; φ(x) 6= 0} where φ does not vanish. By C∞ c (IR) we denote the space of continuous functions with compact support, having continuous derivatives ...

Fixed point theorems for generalized Lipschitzian semigroups are proved in puniformly convex Banach spaces and in uniformly convex Banach spaces. As applications, its corollaries are given in a Hilbert space, in Lp spaces, in Hardy space Hp , and in Sobolev spaces Hk,p , for 1<p <∞ and k≥ 0.

Abstract Some recent results on the theory of fractional Orlicz–Sobolev spaces are surveyed. They concern Sobolev type embeddings for these with an optimal Orlicz target, related Hardy inequalities, and criteria compact embeddings. The limits when smoothness parameter $$s\in (0,1)$$ s ? <mml:m...

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....