Relationship Between Matuszewska-orlicz, Semenov and Simonenko Indices of F-functions
We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an Lp-space (p < ∞). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.
We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an -space (). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.
On décrit de diverses façons les fermetures respectives, dans l’espace et dans sa version locale , de l’ensemble des fonctions à support compact et de l’ensemble des fonctions à support compact. Certains de ces résultats sont nouveaux; d’autres, considérés comme classiques, ne semblent pas avoir fait l’objet de publication. Des contre-exemples permettent de vérifier la diversité des sous-espaces considérés.
In connection with the classes of weights (see [K-T] and [B-K]), we study, in the context of Orlicz spaces, the corresponding reverse-Hölder classes . We prove that when ϕ is and has lower index greater than one, the class coincides with some reverse-Hölder class . For more general ϕ we still get although the intersection of all these gives a proper subset of .
We introduce some practical calculation of the Riesz angles in Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm. For an -function whose index function is monotonous, the exact value of the Orlicz sequence space with Luxemburg norm is or . The Riesz angles of Orlicz space with Orlicz norm has the estimation .
In this paper, the criteria of strong roughness, roughness and pointwise roughness of Orlicz norm and Luxemburg norm on Musielak-Orlicz function spaces are obtained.
We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.