A mean ergodic theorem for a contraction semigroup in Lebesgue space
A minimal regular ring extension of C(X)
Let G(X) denote the smallest (von Neumann) regular ring of real-valued functions with domain X that contains C(X), the ring of continuous real-valued functions on a Tikhonov topological space (X,τ). We investigate when G(X) coincides with the ring of continuous real-valued functions on the space , where is the smallest Tikhonov topology on X for which and is von Neumann regular. The compact and metric spaces for which are characterized. Necessary, and different sufficient, conditions...
A modular convergence theorem for certain nonlinear integral operators with homogeneous kernel.
A multilinear interpolation theorem
A multiplicative embedding inequality in Orlicz--Sobolev spaces.
A multiplier in Besov spaces which is not a multiplier in Lebesgue spaces
A multiplier theorem on weighted Orlicz spaces
A necessary and sufficient condition for existence of extremal functions of a linear functional on .
A negative result in differentiation theory
A Neumann problem with the -Laplacian on a solid torus in the critical of supercritical case.
A new approach to function spaces on quasi-metric spaces.
A new approach to Young measure theory, relaxation and convergence in energy
A new characterization of the interpolation spaces between L... and L...
A new characterization of the Sobolev space
The purpose of this paper is to provide a new characterization of the Sobolev space . We also show a new proof of the characterization of the Sobolev space , 1 ≤ p < ∞, in terms of Poincaré inequalities.
A new convexity property that implies a fixed point property for
In this paper we prove a new convexity property for L₁ that resembles uniform convexity. We then develop a general theory that leads from the convexity property through normal structure to a fixed point property, via a theorem of Kirk. Applying this theory to L₁, we get the following type of normal structure: any convex subset of L₁ of positive diameter that is compact for the topology of convergence locally in measure, must have a radius that is smaller than its diameter. Indeed, a stronger result...
A new extension of Komlós' theorem in infinite dimensions. Application: Weak compactness in .
A new framework for generalized Besov-type and Triebel-Lizorkin-type spaces [Book]
A new function space and applications
We define a new function space , which contains in particular BMO, BV, and , . We investigate its embedding into Lebesgue and Marcinkiewicz spaces. We present several inequalities involving norms of integer-valued functions in . We introduce a significant closed subspace, , of , containing in particular VMO and , . The above mentioned estimates imply in particular that integer-valued functions belonging to are necessarily constant. This framework provides a “common roof” to various,...
A new look on Hankel forms over Fock space
A New Proof of the Fundamental Lemma of Interpolation Theory.