Valdivia compacta and subspaces of C(K) spaces.
Variable Besov and Triebel--Lizorkin spaces.
Variable exponent Fock spaces
We introduce variable exponent Fock spaces and study some of their basic properties such as boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality. We also prove that under the global log-Hölder condition, the variable exponent Fock spaces coincide with the classical ones.
Variable exponent Sobolev spaces with zero boundary values
We study different definitions of the first order variable exponent Sobolev space with zero boundary values in an open subset of .
Variable exponent trace spaces
The trace space of consists of those functions on ℝⁿ that can be extended to functions of (as in the fixed-exponent case). Under the assumption that p is globally log-Hölder continuous, we show that the trace space depends only on the values of p on the boundary. In our main result we show how to define an intrinsic norm for the trace space in terms of a sharp-type operator.
Variable Lebesgue norm estimates for BMO functions
In this paper, we are going to characterize the space through variable Lebesgue spaces and Morrey spaces. There have been many attempts to characterize the space by using various function spaces. For example, Ho obtained a characterization of with respect to rearrangement invariant spaces. However, variable Lebesgue spaces and Morrey spaces do not appear in the characterization. One of the reasons is that these spaces are not rearrangement invariant. We also obtain an analogue of the well-known...
Variable Sobolev capacity and the assumptions on the exponent
In a recent article the authors showed that it is possible to define a Sobolev capacity in variable exponent Sobolev space. However, this set function was shown to be a Choquet capacity only under certain assumptions on the variable exponent. In this article we relax these assumptions.
Variables aléatoires échangeables et espaces d'Orlicz
Variables aléatoires échangeables et espaces d'Orlicz (suite)
Variational fractals
Variational inequalities for energy functionals with nonstandard growth conditions.
Variational inequalities of strongly nonlinear elliptic operators of infinite order.
Variational inequalities of strongly nonlinear elliptic operators of infinite order.
Variational problems on classes of rearrangements and multiple configurations for steady vortices
Variations on a theme of Beurling.
Variations on the Banach-Stone theorem.
Variations on Yano's extrapolation theorem.
We give very short and transparent proofs of extrapolation theorems of Yano type in the framework of Lorentz spaces. The decomposition technique developed in Edmunds-Krbec (2000) enables us to obtain known and new results in a unified manner.
Vector series whose lacunary subseries converge
The area of research of this paper goes back to a 1930 result of H. Auerbach showing that a scalar series is (absolutely) convergent if all its zero-density subseries converge. A series in a topological vector space X is called ℒ-convergent if each of its lacunary subseries (i.e. those with ) converges. The space X is said to have the Lacunary Convergence Property, or LCP, if every ℒ-convergent series in X is convergent; in fact, it is then subseries convergent. The Zero-Density Convergence...
Vector valued measures of bounded mean oscillation.
The duality between H1 and BMO, the space of functions of bounded mean oscillation (see [JN]), was first proved by C. Fefferman (see [F], [FS]) and then other proofs of it were obtained.In this paper we shall study such space in little more detail and we shall consider the H1-BMO duality for vector-valued functions in the more general setting of spaces of homogeneous type (see [CW]).
Vector-valued analytic functions