Related papers: Injective isometries in Orlicz spaces

In this paper, we will improve and generalize inequality of Ostrowski type for mappings whose second derivatives belong to L$_{1}\left(a,b\right) $ . Some well known inequalities can be derived as special cases. In addition, perturbed…

In this paper we study some properties of anisotropic Orlicz and anisotropic Orlicz-Sobolev spaces of vector valued functions for a special class of G-functions. We introduce a variational setting for a class of Lagrangian Systems. We give…

Let $X$ be a compact metric space and $\mathcal M_X$ be the set of isometry classes of compact metric spaces $Y$ such that the Lipschitz distance $d_L(X,Y)$ is finite. We show that $(\mathcal M_X, d_L)$ is not separable when $X$ is a closed…

In this paper, in terms of three types of generalized second-order derivatives of a nonsmooth function, we mainly study the corresponding second-order optimality conditions in a Hilbert space and prove the equivalence among these optimality…

In earlier works on Shape Dynamics (SD), a linear method of solving a particular set of Lichnerowicz-type equations through the implicit function theorem was developed in order to implicitly construct SD's global Hamiltonian and eliminate…

Given a pointed metric space $M$, we study when there exist $n$-dimensional linear subspaces of $\operatorname{Lip}_0(M)$ consisting of strongly norm-attaining Lipschitz functionals, for $n\in\mathbb{N}$. We show that this is always the…

We study coupled non-linear parabolic equations for a fluid described by a material density and a temperature, both functions of space and time. In one dimension, we find some stationary solutions corresponding to fixing the temperature on…

In order to generalize the results of Mazur-Ulam and Vogt, we shall prove that any map T which preserves equality of distance with T(0)=0 between two F-spaces without surjective condition is linear. Then, as a special case linear isometries…

The Orlicz-Brunn-Minkowski theory receives considerable attention recently, and many results in the $L_p$-Brunn-Minkowski theory have been extended to their Orlicz counterparts. The aim of this paper is to develop Orlicz $L_{\phi}$ affine…

A study is made of linear isometries on Fr\'echet spaces for which the metric is given in terms of a sequence of seminorms. This establishes sufficient conditions on the growth of the function that defines the metric in terms of the…

Motivated by the result of Dantas et. al. (2023) that there exist metric spaces for which the set of strongly norm-attaining Lipschitz functions does not contain an isometric copy of $c_0$, we introduce and study a weaker notion of…

We study Birkhoff-James orthogonality and its pointwise symmetry in commutative $C^*$ algebras, i.e., the space of all continuous functions defined on a locally compact Hausdorff space that vanish at infinity. We use this characterization…

Let $(X, T)$ be a topological dynamical system. We show that if each invariant measure of $(X, T)$ gives rise to a measure-theoretic dynamical system that is either: a. rigid along a sequence of "bounded prime volume" or b. admits a…

We give a new characterization of a continuous embedding between two function spaces of type $G\Gamma$. Such spaces are governed by functionals of type \begin{equation*} \|f\|_{G\Gamma(r,q;w,\delta)} := \left(\int_{0}^{L} \left(…

In the present note, we examine the behavior of some homo\-thecy-invariant differentiation basis of rectangles in the plane satisfying the following requirement: for a given rectangle to belong to the basis, the ratio of the largest of its…

This work considers the problem of finding a first-order stationary point of a non-convex function with potentially unbounded smoothness constant using a stochastic gradient oracle. We focus on the class of $(L_0,L_1)$-smooth functions…

In the setting of $\R^d$ with an $n-$dimensional measure $\mu,$ we give several characterizations of Lipschitz spaces in terms of mean oscillations involving $\mu.$ We also show that Lipschitz spaces are preserved by those Calderon-Zygmund…

We prove that $L(X,Y)$ is complemented in $Lip_0(X, Y)$ (via a norm-one projection) provided that $Y$ is a dual space. Next, we introduce a vector-valued Lipschitz-free space $F_Y(X)$, a linear contraction $\beta_X^Y: F_Y(X) \to Y$ and…

In Orlicz spaces generated by convex Orlicz functions a family of norms generated by some lattice norms in $\mathbb{R}^{2}$ are defined and studied. This family of norms includes the family of the p-Amemiya norms ($1\leq p\leq\infty$)…

Let S be a Sobolev or Orlicz-Sobolev space of functions not necessarily vanishing at the boundary of the domain. We give sufficient conditions on a nonnegative function in S in order that its spherical rearrangement ("Schwartz…