Let Gamma be an uncountable cardinal. We construct a real symmetric 1-Lipschitz function on the unit sphere of c(0)(Gamma) whose restriction to any nonseparable subspace is a distortion.
Let Gamma be an uncountable cardinal. We construct a real symmetric 1-Lipschitz function on the unit sphere of c(0)(Gamma) whose restriction to any nonseparable subspace is a distortion.
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when...
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We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of the obstacle and the given exterior force are sufficiently small.
For a Tychonoff space X, we denote by C-p (X) the space of all real-valued continuous functions on X with the topology of pointwise convergence. In this paper we continue to study different selectors for sequences of ...
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For a Tychonoff space X, we denote by C-p (X) the space of all real-valued continuous functions on X with the topology of pointwise convergence. In this paper we continue to study different selectors for sequences of dense sets of C-p (X) started to study in the paper [14]. A set A subset of C-p (X) will be called 1-dense in C-p (X), if for each x is an element of X and an open set W in R there is f is an element of A such that f(x) is an element of W. We give the characterizations of selection principles S-1(A, A), S-fin(A, A) and S-1(S, A) where A - the family of 1-dense subsets of C-p (X);S - the family of sequentially dense subsets of C-p (X), through the selection principles of a space X. In particular, we give the functional characterizations of the Rothberger and Menger properties. (C) 2018 Published by Elsevier B.V.
In their classical work, Sammartino and Caflisch (Commun Math Phys 192(2):433-461, 1998a;Commun Math Phys 192(2):463-491, 1998b) proved the inviscid limit of the incompressible Navier-Stokes equations for well-prepare...
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In their classical work, Sammartino and Caflisch (Commun Math Phys 192(2):433-461, 1998a;Commun Math Phys 192(2):463-491, 1998b) proved the inviscid limit of the incompressible Navier-Stokes equations for well-prepared data with analytic regularity in the half-space. Their proof is based on the detailed construction of Prandtl's boundary layer asymptotic expansions. In this paper, we give a direct proof of the inviscid limit for general analytic data without having to construct Prandtl's boundary layer correctors. Our analysis makes use of the boundary vorticity formulation and the abstract Cauchy-Kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity.
In this article, we study the weighted composition operators preserving the class p(alpha) of analytic functions subordinate to (1 + alpha z)/(1 - z) for vertical bar alpha vertical bar <= 1, alpha not equal -1. So...
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In this article, we study the weighted composition operators preserving the class p(alpha) of analytic functions subordinate to (1 + alpha z)/(1 - z) for vertical bar alpha vertical bar <= 1, alpha not equal -1. Some of its consequences and examples for some special cases are presented.
We prove that a local version of Khintchine inequality holds for arbitrary rearrangement invariant (r.i.) spaces on an non-empty open set . For this, we give a definition of local r.i. space which is compatible with t...
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We prove that a local version of Khintchine inequality holds for arbitrary rearrangement invariant (r.i.) spaces on an non-empty open set . For this, we give a definition of local r.i. space which is compatible with the notion of systems equivalent in distribution and prove that the Rademacher system on an non-empty open set E is equivalent in distribution to on [0, 1], with N depending on E. The result can be generalized to a wider class of sets.
We present examples of holomorphic functions that vanish to infinite order at points at the boundary of their domain of definition. They give rise to examples of Dirichlet minimizing Q-valued functions indicating that...
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We present examples of holomorphic functions that vanish to infinite order at points at the boundary of their domain of definition. They give rise to examples of Dirichlet minimizing Q-valued functions indicating that "higher"-regularity boundary results are difficult. Furthermore we discuss some implication to branching and vanishing phenomena in the context of minimal surfaces, Q-valued functions, and unique continuation.
In this work we show endpoint boundedness properties of pseudo-differential operators of type (rho, rho), 0 < rho < 1, on Triebel-Lizorkin and Besov spaces. Our results are sharp and they also cover operators de...
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In this work we show endpoint boundedness properties of pseudo-differential operators of type (rho, rho), 0 < rho < 1, on Triebel-Lizorkin and Besov spaces. Our results are sharp and they also cover operators defined by compound symbols. (C) 2017 Elsevier Inc. All rights reserved.
We establish an extension of the Banach-Stone theorem to a class of isomorphisms more general than isometries in a noncompact framework. Some applications are given. In particular, we give a canonical representation o...
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We establish an extension of the Banach-Stone theorem to a class of isomorphisms more general than isometries in a noncompact framework. Some applications are given. In particular, we give a canonical representation of some (not necessarily linear) operators between products of function spaces. Our results are established for an abstract class of function spaces included in the space of all continuous and bounded functions defined on a complete metric space.
Let F be a Banach space of continuous functions over a connected locally compact space X. We present several sufficient conditions on F guaranteeing that the only multiplication operators on F that are surjective isom...
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Let F be a Banach space of continuous functions over a connected locally compact space X. We present several sufficient conditions on F guaranteeing that the only multiplication operators on F that are surjective isometrics are scalar multiples of the identity. The conditions are given via the properties of the inclusion operator from F into C (X), as well as in terms of geometry of F. An important tool in our investigation is the notion of Birkhoff Orthogonality. (C) 2019 Elsevier Inc. All rights reserved.
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