Related papers: Bootstrapping the Mazur--Orlicz--K\"onig theorem

The problem involving the extension of functions from a certain class and defined on subdomains of the ambient space to the whole space is an old and a well investigated theme in analysis. A related question whether the extensions that…

In this paper, we shall establish Banach-Stone type theorems on spaces of uniformly continuous and lipschitz continuous pseudometrics.

The Orlicz-Brunn-Minkowski theory, introduced by Lutwak, Yang, and Zhang, is a new extension of the classical Brunn-Minkowski theory. It represents a generalization of the $L_p$-Brunn-Minkowski theory, analogous to the way that Orlicz…

We prove multiplier theorems on rank one noncompact symmetric spaces which improve aspects of existing results. A common theme of our main results is that we partially drop specific assumptions on the multiplier function such as a…

Let $K$ be a compact Hausdorff space and let $H$ be a real or complex Hilbert space with dim$(H_\mathbb{R})\geq 2$. We prove that the space $C(K,H)$ of all $H$-valued continuous functions on $K$, equipped with the supremum norm, satisfies…

In this paper we prove a gap theorem for K\"ahler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author. We also prove a Liouville theorem for…

The main purpose of this paper is to generalize the celebrated L${}^2$ extension theorem of Ohsawa-Takegoshi in several directions : the holomorphic sections to extend are taken in a possibly singular hermitian line bundle, the subvariety…

In this article we prove a theorem of Ohsawa-Takegoshi type on compact K\"ahler manifolds. Our arguments follow the "standard" approach for this kind of extension results; however, there are many complications arising from the…

We show that a considerable part of the theory of (ultra)distributions and hyperfunctions can be extended to more singular generalized functions, starting from an angular localizability notion introduced previously. Such an extension is…

The main aim of this work is to give a general approach to the celebrated Kahane-Salem-Zygmund inequalities. We prove estimates for exponential Orlicz norms of averages $\sup_{1\le j \leq N} \big |\sum_{1 \leq i \leq K}\gamma_i(\cdot)…

In this note a far extension of the Banach fixed point theorem is proved.

We discuss various known generalizations of the classical Hartogs' extension theorem on Stein spaces with arbitrary singularities and present an analytic proof based on d-bar methods.

We prove that a $\Phi$-function can be extended from a domain $\Omega$ to all of $\mathbb R^n$ while preserving crucial properties for harmonic analysis on the generalized Orlicz space $L^\Phi$.

We prove a generalized implicit function theorem for Banach spaces, without the usual assumption that the subspaces involved being complemented. Then we apply it to the problem of parametrization of fibers of differentiable maps, the Lie…

We give a nonlinear representation of the duals for a class of Banach spaces. This leads to classroom-friendly proofs of the classical representation theorems $H'=H$ and $(L^p)'=L^q$. Our proofs extend to a family of Orlicz spaces, and…

We introduce the concept of shifting distance functions, and we establish a new fixed point theorem which generalizes the Banach contraction principle. An example is provided to illustrate our result.

We give an exposition of Novodvorskii's theorem in Banach algebra K-theory, asserting that the Gelfand transform for a commutative Banach algebra induces an isomorphism in topological K-theory.

K\"onig's lemma is a fundamental result about trees with countless applications in mathematics and computer science. In contrapositive form, it states that if a tree is finitely branching and well-founded (i.e. has no infinite paths), then…

Due to the work of many authors in the last decades, given an algebraic orbifold (smooth proper Deligne-Mumford stack with trivial generic stabilizer), one can construct its orbifold Chow ring and orbifold Grothendieck ring, and relate them…

We obtain similar types of conclusions as that of Br\"{u}ck [1] for two differential polynomials which in turn radically improve and generalize several existing results. Moreover, a number of examples have been exhibited to justify the…