Alireza Ranjbar-Motlagh

Sharif University of Technology | SHARIF · Department of Mathematical Science

Мы исследуем возможность выполнения однородного и неоднородного неравенств типа Нэша в случае абстрактных пространств.

The purpose of this article is to study the Besov type function spaces for maps which are defined on abstract metric-measure spaces. We extend some of the embedding theorems of the classical Besov spaces to the setting of abstract spaces.

This article characterizes the isometries between spaces of all differentiable functions from a compact interval of the real line into a strictly convex Banach space. 1. Introduction The main purpose of this article is to characterize the isometries of the space of all (continuously) differentiable functions from a compact interval of the real lin...

The purpose of this article is to study the isometries between vector-valued absolutely continuous function spaces, over compact subsets of the real line. Indeed, under certain conditions, it is shown that such isometries can be represented as a weighted composition operator. 1. Introduction Suppose that and are Banach spaces (real or complex) and...

The main purpose of this article is to generalize a characterization of Lipschitz functions in the context of metric-measure spaces. The results are established in the class of metric-measure spaces which satisfy a strong version of the doubling (Bishop-Gromov regularity) condition. Indeed, we establish a necessary and sufficient condition in order...

In this article, we describe isometries over the Lipschitz spaces under certain conditions. Indeed, we provide a unified proof for the main results of 3 and 5 in a more general setting. Finally, we extend our results for some other functions spaces like the space of vector‐valued little Lipschitz maps and pointwise Lipschitz maps.

The main purpose of this article is to generalize a recent result about isometries of Lipschitz spaces. Botelho, Fleming and Jamison [2] described surjective linear isometries between vector-valued Lipschitz spaces under certain conditions. In this article, we extend the main result of [2] by removing the quasi-sub-reflexivity condition from Banach...

The main purpose of this article is to generalize a characterization of constant functions to the context of metric-measure spaces. In fact, we approximate a measurable function, in terms of a certain integrability condition, by Lipschitz functions. Then, similar to Brezis (2002) [2], we establish a necessary and sufficient condition in order that...

The main purpose of this article is to generalize a theorem about the size of minimal submanifolds in Euclidean spaces. In fact, we state and prove a non-existence theorem about harmonic maps from a stochastically complete manifold into a cone type domain. The proof is based on a generalized version of the maximum principle applied to the Lapalace-...

Let f:M⟶M¯ be an isometric immersion between Riemannian manifolds. For certain conditions on M and M¯ in terms of curvatures and external diameter, we extend the non-embedding theorem of Chern and Kuiper to the isometric immersions of non-compact manifolds. Also, our results generalize and improve the main results of Jorge and Koutroufiotis [L. Jor...

The purpose of this paper is to prove an embedding theorem for Sobolev type functions whose gradients are in a Lorentz space, in the framework of abstract metric-measure spaces. We then apply this theorem to prove absolute continuity and differentiability of such functions.

The main purpose of this article is to generalize a theorem of Stepanov which provides a necessary and sufficient condition for almost everywhere differentiability of functions over Euclidean spaces. We state and prove an Lp-type generalization of the Stepanov theorem and then we extend it to the context of Orlicz spaces. Then, this generalized Rad...

The purpose of this paper is to generalize the Liouville theorem for functions which are defined on the complete Riemannian manifolds. Then, we apply it to the isometric immersions between complete Riemannian manifolds in order to obtain an estimate for the size of the image of immersions in terms of the supremum of the length of their mean curvatu...

The main purpose of this article is to extend an L p-type generalization of Stepanov's differentiability theorem in metric-measure space. This generalized Stepanov type theorem is applied to the Sobolev and bounded variation functions in order to show the L p-type generalized differentiability for such functions. The proof of this generalized diffe...

The Poincaré inequality is generalised to metric-measure spaces which support a strong version of the doubling condition. This generalises the Poincaré inequality for manifolds whose Ricci curvature is bounded from below and metric-measure spaces which satisfy the measure contraction property.

The Poincaré inequality is extended to uniformly doubling metric-measure spaces which satisfy a version of the triangle comparison property. The proof is based on a generalization of the change of variables formula.

Letf:M [`(M)]\bar M be an isometric immersion between Riemannian manifolds. The purpose of this paper is to find the minimum possible conditions onM and [`(M)]\bar M (in the terms of curvatures and external diameter) in order to the image off be contained in a sphere. Our results generalize the other authors work in three major steps, domain, range...

In this paper we investigate the action of a group on a hyperbolic space where the subgroups are geometrically finite. Several well-know results about hyperbolic and free groups follows as speacial cases. The proofs are based on the induced action of groups on the boundary of hyperbolic spaces.