Weighted Hardy-type inequalities in Orlicz spaces

Orlicz-hardy Inequalities

We relate Orlicz-Hardy inequalities on a bounded Euclidean domain to certain fatness conditions on the complement. In the case of certain log-scale distortions of Ln, this relationship is necessary and sufficient, thus extending results of Ancona, Lewis, and Wannebo. 0. Introduction Suppose Ω ⊂ R is a bounded domain and let d(x) = dist(x, ∂Ω). We consider integral Hardy inequalities (0.1) ∀u ∈ ...

Compact composition operators on Hardy-Orlicz and weighted Bergman-Orlicz spaces on the ball

Using recent characterizations of the compactness of composition operators on HardyOrlicz and Bergman-Orlicz spaces on the ball ([2, 3]), we first show that a composition operator which is compact on every Hardy-Orlicz (or Bergman-Orlicz) space has to be compact on H∞. Then, although it is well-known that a map whose range is contained in some nice Korányi approach region induces a compact comp...

Korn Inequalities In Orlicz Spaces

We use gradient estimates for solutions of elliptic equations to obtain Korn’s inequality for fields with zero trace from Orlicz–Sobolev classes. As outlined for example in the monographs of Málek, Nečas, Rokyta, Růžička [MNRR], of Duvaut and Lions [DL] and of Zeidler [Ze], the well-posedness of many variational problems arising in fluid mechanics or in the mechanics of solids heavily depends o...

Maximal Inequalities of Kahane-Khintchine’s Type in Orlicz Spaces

Several maximal inequalities of Kahane-Khintchine’s type in certain Orlicz spaces are proved. The method relies upon Lévy’s inequality and the technique established in [14] which is obtained by Haagerup-Young-Stechkin’s best possible constants in the classical Khintchine inequalities. Moreover by using Donsker’s invariance principle it is shown that the numerical constant in the inequality dedu...

Hardy Inequalities in Function Spaces